Pub Date : 2022-01-01DOI: 10.14232/ejqtde.2022.1.26
S. Stević
We present thirty-six classes of three-dimensional systems of difference equations of the hyperbolic-cotangent type which are solvable in closed form.
本文给出了36类可解的双曲-余切型三维差分方程组。
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Pub Date : 2022-01-01DOI: 10.14232/ejqtde.2022.1.34
P. Korman, D. Schmidt
<jats:p>We reduce solution of the Dirichlet problem (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns="http://www.w3.org/1998/Math/MathML"> <mml:mi>x</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mi>D</mml:mi> <mml:mo>⊂<!-- ⊂ --></mml:mo> <mml:msup> <mml:mi>R</mml:mi> <mml:mi>m</mml:mi> </mml:msup> </mml:math>) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <mml:mi mathvariant="normal">Δ<!-- Δ --></mml:mi> <mml:mi>u</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>+</mml:mo> <mml:mi>a</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mi>u</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>f</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mspace width="1em" /> <mml:mstyle displaystyle="false" scriptlevel="0"> <mml:mtext>in </mml:mtext> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>D</mml:mi> </mml:mrow> </mml:mstyle> <mml:mo>,</mml:mo> <mml:mspace width="2em" /> <mml:mi>u</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mspace width="1em" /> <mml:mstyle displaystyle="false" scriptlevel="0"> <mml:mtext>on </mml:mtext> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">∂<!-- ∂ --></mml:mi> <mml:mi>D</mml:mi> </mml:mrow> </mml:mstyle> </mml:math> to iterative solution of a simpler problem <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <mml:mi mathvariant="normal">Δ<!-- Δ --></mml:mi> <mml:mi>u</mml:mi> <mml:mo>=</mml:mo> <mml:mi>f</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mspace width="thickmathspace" /> <mml:mspace width="thickmathspace" /> <mml:mstyle displaystyle="false" scriptlevel="0"> <mml:mtext>in </mml:mtext> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>D</mml:mi> </mml:mrow> </mml:mstyle> <mml:mo>,</mml:mo> <mml:mspace width="thickmathspace" /> <mml:mspace width="thickmathspace" /> <mml:mi>u</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mspace width="thickmathspace" /> <mml:mspace width="thickmathspace" /> <mml:mstyle displaystyle="false" scriptlevel="0"> <mml:mtext>on </mml:mtext> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">∂<!-- ∂ --></mml:mi> <mml:mi>D</mml:mi> </mml:mrow> </mml:mstyle> <mml:mspace width="thinmathspace" /> <mml:mo>,</mml:mo> </mml:math> for which one can use either Fourier series or Green's function method. The method is suitable for numerical computations, particularly when one uses Newton's method for semilinear problems
我们将Dirichlet问题(x∈D∧R m) Δ u (x) + a (x) u (x) = f (x)在D中，u = 0在∂D中简化为一个更简单的问题Δ u = f (x)在D中，u = 0在∂D中，可以使用傅里叶级数或格林函数方法。该方法适用于数值计算，特别是当人们使用牛顿方法解决半线性问题Δ u + g (x, u) = 0在D中，u = 0在∂D中，。
{"title":"Iterative solution of elliptic equations","authors":"P. Korman, D. Schmidt","doi":"10.14232/ejqtde.2022.1.34","DOIUrl":"https://doi.org/10.14232/ejqtde.2022.1.34","url":null,"abstract":"<jats:p>We reduce solution of the Dirichlet problem (<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>x</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mi>D</mml:mi> <mml:mo>⊂<!-- ⊂ --></mml:mo> <mml:msup> <mml:mi>R</mml:mi> <mml:mi>m</mml:mi> </mml:msup> </mml:math>) <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"> <mml:mi mathvariant=\"normal\">Δ<!-- Δ --></mml:mi> <mml:mi>u</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>+</mml:mo> <mml:mi>a</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mi>u</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>f</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mspace width=\"1em\" /> <mml:mstyle displaystyle=\"false\" scriptlevel=\"0\"> <mml:mtext>in </mml:mtext> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>D</mml:mi> </mml:mrow> </mml:mstyle> <mml:mo>,</mml:mo> <mml:mspace width=\"2em\" /> <mml:mi>u</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mspace width=\"1em\" /> <mml:mstyle displaystyle=\"false\" scriptlevel=\"0\"> <mml:mtext>on </mml:mtext> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi mathvariant=\"normal\">∂<!-- ∂ --></mml:mi> <mml:mi>D</mml:mi> </mml:mrow> </mml:mstyle> </mml:math> to iterative solution of a simpler problem <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"> <mml:mi mathvariant=\"normal\">Δ<!-- Δ --></mml:mi> <mml:mi>u</mml:mi> <mml:mo>=</mml:mo> <mml:mi>f</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mspace width=\"thickmathspace\" /> <mml:mspace width=\"thickmathspace\" /> <mml:mstyle displaystyle=\"false\" scriptlevel=\"0\"> <mml:mtext>in </mml:mtext> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>D</mml:mi> </mml:mrow> </mml:mstyle> <mml:mo>,</mml:mo> <mml:mspace width=\"thickmathspace\" /> <mml:mspace width=\"thickmathspace\" /> <mml:mi>u</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mspace width=\"thickmathspace\" /> <mml:mspace width=\"thickmathspace\" /> <mml:mstyle displaystyle=\"false\" scriptlevel=\"0\"> <mml:mtext>on </mml:mtext> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi mathvariant=\"normal\">∂<!-- ∂ --></mml:mi> <mml:mi>D</mml:mi> </mml:mrow> </mml:mstyle> <mml:mspace width=\"thinmathspace\" /> <mml:mo>,</mml:mo> </mml:math> for which one can use either Fourier series or Green's function method. The method is suitable for numerical computations, particularly when one uses Newton's method for semilinear problems ","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66584786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.14232/ejqtde.2022.1.47
Equations Jorge Rodríguez–López, R. Precup, C. Gheorghiu
The paper deals with the existence and localization of positive radial solutions for stationary partial differential equations involving a general ϕ -Laplace operator in the annulus. Three sets of boundary conditions are considered: Dirichlet–Neumann, Neumann–Dirichlet and Dirichlet–Dirichlet. The results are based on the homotopy version of Krasnosel'skii's fixed point theorem and Harnack type inequalities, first established for each one of the boundary conditions. As a consequence, the problem of multiple solutions is solved in a natural way. Numerical experiments confirming the theory, one for each of the three sets of boundary conditions, are performed by using the MATLAB object-oriented package Chebfun.
{"title":"On the localization and numerical computation of positive radial\u0000 solutions for \u0000 ϕ\u0000 \u0000 \u0000-Laplace equations in the annulus","authors":"\t\tEquations\t\t\tJorge Rodríguez–López, R. Precup, C. Gheorghiu","doi":"10.14232/ejqtde.2022.1.47","DOIUrl":"https://doi.org/10.14232/ejqtde.2022.1.47","url":null,"abstract":"The paper deals with the existence and localization of positive radial solutions for stationary partial differential equations involving a general ϕ -Laplace operator in the annulus. Three sets of boundary conditions are considered: Dirichlet–Neumann, Neumann–Dirichlet and Dirichlet–Dirichlet. The results are based on the homotopy version of Krasnosel'skii's fixed point theorem and Harnack type inequalities, first established for each one of the boundary conditions. As a consequence, the problem of multiple solutions is solved in a natural way. Numerical experiments confirming the theory, one for each of the three sets of boundary conditions, are performed by using the MATLAB object-oriented package Chebfun.","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":"15 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81667728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.14232/ejqtde.2022.1.21
Chao Ji, YongDe Zhang, V. Rǎdulescu
<jats:p>In this paper, we are concerned with the following magnetic Schrödinger–Poisson system <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <mml:mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mml:mtr> <mml:mtd> <mml:mrow> <mml:mo>{</mml:mo> <mml:mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mml:mtr> <mml:mtd> <mml:mo>−<!-- − --></mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="normal">∇<!-- ∇ --></mml:mi> <mml:mo>+</mml:mo> <mml:mi>i</mml:mi> <mml:mi>A</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mi>u</mml:mi> <mml:mo>+</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mi>λ<!-- λ --></mml:mi> <mml:mi>V</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mi>u</mml:mi> <mml:mo>+</mml:mo> <mml:mi>ϕ<!-- ϕ --></mml:mi> <mml:mi>u</mml:mi> <mml:mo>=</mml:mo> <mml:mi>α<!-- α --></mml:mi> <mml:mi>f</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>u</mml:mi> <mml:mo>|</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mi>u</mml:mi> <mml:mo>+</mml:mo> <mml:mo fence="false" stretchy="false">|</mml:mo> <mml:mi>u</mml:mi> <mml:msup> <mml:mo fence="false" stretchy="false">|</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> <mml:mi>u</mml:mi> <mml:mo>,</mml:mo> </mml:mtd> <mml:mtd>
在本文中，我们关注以下磁性Schrödinger-Poisson系统{−(∇+ i A (x)) 2u + (λ V)(x) + 1) u + φ u = α f (| u | 2) u + | u在r3中，−Δ ϕ = u 2，在R 3中，其中λ > 0为参数，f为亚临界非线性，势V: r3→R为连续函数，验证某些条件，磁势a∈L L o c2 (r3, r3)。假设V (x)的零集有几个孤立的连通分量Ω 1，…，Ω k，使得Ω j的内部是非空的，∂Ω j是光滑的，其中j∈{1，…，k}，那么对于λ >足够大，我们使用变分方法证明了上述系统至少有2k−1个多凹凸解。
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Pub Date : 2022-01-01DOI: 10.14232/ejqtde.2022.1.2
Abdulaziz Almaslokh, C. Qian
<jats:p>Consider the following higher order difference equation <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"> <mml:mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mml:mtr> <mml:mtd> <mml:mi>x</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>a</mml:mi> <mml:mi>x</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>+</mml:mo> <mml:mi>b</mml:mi> <mml:mi>f</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> <mml:mo>+</mml:mo> <mml:mi>c</mml:mi> <mml:mi>f</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mi>k</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> <mml:mo>,</mml:mo> <mml:mspace width="2em" /> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mo>…<!-- … --></mml:mo> </mml:mtd> </mml:mtr> </mml:mtable> </mml:math> where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> </mml:math> and <jats:italic>c</jats:italic> are constants with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>0</mml:mn> <mml:mo><</mml:mo> <mml:mi>a</mml:mi> <mml:mo><</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>0</mml:mn> <mml:mo>≤<!-- ≤ --></mml:mo> <mml:mi>b</mml:mi> <mml:mo><</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>0</mml:mn> <mml:mo>≤<!-- ≤ --></mml:mo> <mml:mi>c</mml:mi> <mml:mo><</mml:mo> <mml:mn>1</mml:mn> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>a</mml:mi> <mml:mo>+</mml:mo> <mml:mi>b</mml:mi> <mml:mo>+</mml:mo> <mml:mi>c</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>f</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mi>C</mml:mi> <mml:mo stretchy="false">[</mml:mo> <mml:mo stretchy="false">[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi mathvariant="normal">∞<!-- ∞ --></mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>,</mml:mo> <mml:mo stretchy="
考虑以下高阶差分方程x (n + 1) = a x (n) + b f (x (n)) + c f (x (n−k))， n = 0,1，…b和c为常数，取值为0 a 1,0≤b 1,0≤c 1，且a + b + c = 1, f∈c[[0，∞)，[0，∞)]，f (x) > 0, x > 0, k为正整数。本文的目的是研究该方程正解的全局吸引性及其在某些种群模型中的应用。
{"title":"On global attractivity of a higher order difference equation and its applications","authors":"Abdulaziz Almaslokh, C. Qian","doi":"10.14232/ejqtde.2022.1.2","DOIUrl":"https://doi.org/10.14232/ejqtde.2022.1.2","url":null,"abstract":"<jats:p>Consider the following higher order difference equation <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"> <mml:mtable columnalign=\"right left right left right left right left right left right left\" rowspacing=\"3pt\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" displaystyle=\"true\"> <mml:mtr> <mml:mtd> <mml:mi>x</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>a</mml:mi> <mml:mi>x</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>+</mml:mo> <mml:mi>b</mml:mi> <mml:mi>f</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>+</mml:mo> <mml:mi>c</mml:mi> <mml:mi>f</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mi>k</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>,</mml:mo> <mml:mspace width=\"2em\" /> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mo>…<!-- … --></mml:mo> </mml:mtd> </mml:mtr> </mml:mtable> </mml:math> where <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> </mml:math> and <jats:italic>c</jats:italic> are constants with <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mn>0</mml:mn> <mml:mo><</mml:mo> <mml:mi>a</mml:mi> <mml:mo><</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>0</mml:mn> <mml:mo>≤<!-- ≤ --></mml:mo> <mml:mi>b</mml:mi> <mml:mo><</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>0</mml:mn> <mml:mo>≤<!-- ≤ --></mml:mo> <mml:mi>c</mml:mi> <mml:mo><</mml:mo> <mml:mn>1</mml:mn> </mml:math> and <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>a</mml:mi> <mml:mo>+</mml:mo> <mml:mi>b</mml:mi> <mml:mo>+</mml:mo> <mml:mi>c</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:math>, <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>f</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mi>C</mml:mi> <mml:mo stretchy=\"false\">[</mml:mo> <mml:mo stretchy=\"false\">[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi mathvariant=\"normal\">∞<!-- ∞ --></mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>,</mml:mo> <mml:mo stretchy=\"","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66584024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.14232/ejqtde.2022.1.33
Michal Feckan, J. Pacuta
We study existence and local uniqueness of periodic solutions of nonlinear functional differential equations of first order with small delays. Bifurcations of periodic and bounded solutions of particular periodically forced second-order equations with small delays are investigated as well.
{"title":"Periodic and bounded solutions of functional differential equations with small delays","authors":"Michal Feckan, J. Pacuta","doi":"10.14232/ejqtde.2022.1.33","DOIUrl":"https://doi.org/10.14232/ejqtde.2022.1.33","url":null,"abstract":"We study existence and local uniqueness of periodic solutions of nonlinear functional differential equations of first order with small delays. Bifurcations of periodic and bounded solutions of particular periodically forced second-order equations with small delays are investigated as well.","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66584653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.14232/ejqtde.2022.1.7
Sylvia Novo, Víctor M. Villarragut
The asymptotic behavior of the trajectories of compartmental systems with a general set of admissible initial data is studied. More precisely, these systems are described by families of monotone nonautonomous neutral functional differential equations with nonautonomous operator. We show that the solutions asymptotically exhibit the same recurrence properties as the transport functions and the coefficients of the neutral operator. Conditions for the cases in which the delays in the neutral and non neutral parts are different, as well as for other cases unaddressed in the previous literature are also obtained.
{"title":"Long-term behavior of nonautonomous neutral compartmental systems","authors":"Sylvia Novo, Víctor M. Villarragut","doi":"10.14232/ejqtde.2022.1.7","DOIUrl":"https://doi.org/10.14232/ejqtde.2022.1.7","url":null,"abstract":"The asymptotic behavior of the trajectories of compartmental systems with a general set of admissible initial data is studied. More precisely, these systems are described by families of monotone nonautonomous neutral functional differential equations with nonautonomous operator. We show that the solutions asymptotically exhibit the same recurrence properties as the transport functions and the coefficients of the neutral operator. Conditions for the cases in which the delays in the neutral and non neutral parts are different, as well as for other cases unaddressed in the previous literature are also obtained.","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66585371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.14232/ejqtde.2022.1.1
L. Barreira, C. Valls
We give two new characterizations of the notion of Lyapunov regularity in terms of the lower and upper exponential growth rates of the singular values. These characterizations motivate the introduction of new regularity coefficients. In particular, we establish relations between these regularity coefficients and the Lyapunov regularity coefficient. Moreover, we construct explicitly bounded sequences of matrices attaining specific values of the new regularity coefficients.
{"title":"New regularity coefficients","authors":"L. Barreira, C. Valls","doi":"10.14232/ejqtde.2022.1.1","DOIUrl":"https://doi.org/10.14232/ejqtde.2022.1.1","url":null,"abstract":"We give two new characterizations of the notion of Lyapunov regularity in terms of the lower and upper exponential growth rates of the singular values. These characterizations motivate the introduction of new regularity coefficients. In particular, we establish relations between these regularity coefficients and the Lyapunov regularity coefficient. Moreover, we construct explicitly bounded sequences of matrices attaining specific values of the new regularity coefficients.","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66583434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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