Pub Date : 2023-01-01DOI: 10.14232/ejqtde.2023.1.28
Fanni Kádár, G. Stépán
Direct spring operated pressure relief valves connected to a constantly charged vessel and a downstream pipe have a complex dynamics. The vessel-valve subsystem is described with an autonomous system of ordinary differential equations, while the presence of the pipe adds two partial differential equations to the mathematical model. The partial differential equations are transformed to a delay algebraic equation coupled to the ordinary differential equations. Due to a square root nonlinearity, the system is implicit. The linearized system can be transformed to a standard system of neutral delay differential equations (NDDEs) having more elaborated literature than the delay algebraic equations. First, the different forms of the mathematical model are presented, then the transformation of the linearized system is conducted. The paper aims at introducing this unusual mathematical model of an engineering system and inducing research focusing on the methodology to carry out bifurcation analysis in implicit NDDEs.
{"title":"An implicit system of delay differential algebraic equations from hydrodynamics","authors":"Fanni Kádár, G. Stépán","doi":"10.14232/ejqtde.2023.1.28","DOIUrl":"https://doi.org/10.14232/ejqtde.2023.1.28","url":null,"abstract":"Direct spring operated pressure relief valves connected to a constantly charged vessel and a downstream pipe have a complex dynamics. The vessel-valve subsystem is described with an autonomous system of ordinary differential equations, while the presence of the pipe adds two partial differential equations to the mathematical model. The partial differential equations are transformed to a delay algebraic equation coupled to the ordinary differential equations. Due to a square root nonlinearity, the system is implicit. The linearized system can be transformed to a standard system of neutral delay differential equations (NDDEs) having more elaborated literature than the delay algebraic equations. First, the different forms of the mathematical model are presented, then the transformation of the linearized system is conducted. The paper aims at introducing this unusual mathematical model of an engineering system and inducing research focusing on the methodology to carry out bifurcation analysis in implicit NDDEs.","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66586206","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 : 2023-01-01DOI: 10.14232/ejqtde.2023.1.34
Hao Zhang, Na Wang
This paper discusses a class of nonlinear singular perturbation problems with Robin boundary values in critical cases. By using the boundary layer function method and successive approximation theory, the corresponding asymptotic expansions of small parameters are constructed, and the existence of uniformly efficient smooth solutions is proved. Meanwhile, we give a concrete example to prove the validity of our results.
{"title":"A class of singularly perturbed Robin boundary value problems in critical case","authors":"Hao Zhang, Na Wang","doi":"10.14232/ejqtde.2023.1.34","DOIUrl":"https://doi.org/10.14232/ejqtde.2023.1.34","url":null,"abstract":"This paper discusses a class of nonlinear singular perturbation problems with Robin boundary values in critical cases. By using the boundary layer function method and successive approximation theory, the corresponding asymptotic expansions of small parameters are constructed, and the existence of uniformly efficient smooth solutions is proved. Meanwhile, we give a concrete example to prove the validity of our results.","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66586394","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}
这篇文章是关心世事with the跟踪nonlocal组合连接在一起的问题nonlinearities(−Δ ) s u =−α | u | q−2 u +βu +γ | u | 2 s ∗ 在−2 u在Ω,u = 0 R N∖Ω,哪里s∈(0,1),N > 2 s,Ω⊂ R N a bounded C是 1 , Lipschitz 1和域边界,α是一个积极,q参数∈(1、2)、β和γ是阳性constants 2 s ∗ = 2 N / ( N s−2)是《fractional连接exponent。为γs > 0,如果N⩾4和0βλ 1 , s,或者N > 2和β⩾λ 1 , s,我们的节目就是《地面possesses a state university)溶液问题当α是足够小。
Pub Date : 2023-01-01DOI: 10.14232/ejqtde.2023.1.30
B. Baculíková
In this paper, we offer new technique for investigation of the even order linear differential equations of the form (E)y(n)(t)=p(t)y(τ(t)). We establish new criteria for bounded and unbounded oscillation of (E) which improve a number of related ones in the literature. Our approach essentially involves establishing stronger monotonicities for the positive solutions of (E) than those presented in known works. We illustrate the improvement over known results by applying and comparing our technique with the other known methods on the particular examples.
本文给出了研究形式为(E) y (n) (t) = p (t) y (τ (t))的偶阶线性微分方程的新方法。我们建立了(E)的有界和无界振荡的新判据，改进了文献中有关的判据。我们的方法本质上涉及建立(E)的正解比已知作品中提出的更强的单调性。我们通过将我们的技术与其他已知方法在特定示例上的应用和比较来说明对已知结果的改进。
{"title":"New monotonicity properties and oscillation of $n$-order functional differential equations with deviating argument","authors":"B. Baculíková","doi":"10.14232/ejqtde.2023.1.30","DOIUrl":"https://doi.org/10.14232/ejqtde.2023.1.30","url":null,"abstract":"<jats:p>In this paper, we offer new technique for investigation of the even order linear differential equations of the form <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"> <mml:mtable displaystyle=\"true\"> <mml:mlabeledtr> <mml:mtd id=\"mjx-eqn-E\"> <mml:mrow> <mml:mtext>(</mml:mtext> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>E</mml:mi> </mml:mrow> <mml:mtext>)</mml:mtext> </mml:mrow> </mml:mtd> <mml:mtd> <mml:msup> <mml:mi>y</mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> </mml:msup> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>p</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mi>y</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>τ<!-- τ --></mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>.</mml:mo> </mml:mtd> </mml:mlabeledtr> </mml:mtable> </mml:math> We establish new criteria for bounded and unbounded oscillation of <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow class=\"MathJax_ref\" href=\"#mjx-eqn-E\"> <mml:mrow> <mml:mtext>(</mml:mtext> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>E</mml:mi> </mml:mrow> <mml:mtext>)</mml:mtext> </mml:mrow> </mml:mrow> </mml:math> which improve a number of related ones in the literature. Our approach essentially involves establishing stronger monotonicities for the positive solutions of <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow class=\"MathJax_ref\" href=\"#mjx-eqn-E\"> <mml:mrow> <mml:mtext>(</mml:mtext> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>E</mml:mi> </mml:mrow> <mml:mtext>)</mml:mtext> </mml:mrow> </mml:mrow> </mml:math> than those presented in known works. We illustrate the improvement over known results by applying and comparing our technique with the other known methods on the particular examples.</jats:p>","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66586328","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}
由$Q$ $ prosult激励，Arcoya和Boccardo在[J。Funct。肛门268号(2015年),第五章,1153—1166],我们analyze软弱之行为解决方案 { − Δ p u ε + ε | f ( x ) | u ε = f ( x ) 在 Ω ,u ε = 0 在 ∂ Ω , 当εtends to 0。在这里,Ωdenotes a bounded开放组的 R N (N≥2) ), − Δp u =− d . i v ( | ∇u | p−2 ∇u)是《祸p-Laplacian接线员(1 p∞)和f (x)是一个L 1(Ω)功能。我们在一些节目,以至于这个序列converges sense to u,熵solution》问题 { − Δ p u = f ( x ) 在 Ω , u = 0 在 ∂ Ω .在半线性案例中，我们证明了现有问题的薄弱解决方案。
{"title":"Convergence of weak solutions of elliptic problems with datum in L 1 ","authors":"Antonio Jesús Martínez Aparicio","doi":"10.14232/ejqtde.2023.1.21","DOIUrl":"https://doi.org/10.14232/ejqtde.2023.1.21","url":null,"abstract":"<jats:p>Motivated by the $Q$-condition result proven by Arcoya and Boccardo in [J. Funct. Anal. 268(2015), No. 5, 1153–1166], we analyze the behaviour of the weak solutions <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"> <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:msub> <mml:mi mathvariant=\"normal\">Δ<!-- Δ --></mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:msub> <mml:mi>u</mml:mi> <mml:mi>ε<!-- ε --></mml:mi> </mml:msub> <mml:mo>+</mml:mo> <mml:mi>ε<!-- ε --></mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mi>f</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:msub> <mml:mi>u</mml:mi> <mml:mi>ε<!-- ε --></mml:mi> </mml:msub> <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:mtd> <mml:mtd> <mml:mtext>in </mml:mtext> <mml:mi mathvariant=\"normal\">Ω<!-- Ω --></mml:mi> <mml:mo>,</mml:mo> </mml:mtd> </mml:mtr> <mml:mtr> <mml:mtd> <mml:msub> <mml:mi>u</mml:mi> <mml:mi>ε<!-- ε --></mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mtd> <mml:mtd> <mml:mtext>on </mml:mtext> <mml:mi mathvariant=\"normal\">∂<!-- ∂ --></mml:mi> <mml:mi mathvariant=\"normal\">Ω<!-- Ω --></mml:mi> <mml:mo>,</mml:mo> </mml:mtd> </mml:mtr> </mml:mtable> <mml:mo fence=\"true\" stretchy=\"true\" symmetric=\"true\" /> </mml:mrow> </mml:math> when <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>ε<!-- ε --></mml:mi> </mml:math> tends to <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns=\"http://www.w3.org/1998/Math/MathML\"> <mml:mn>0</mml:mn> </mml:math>. Here, <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi mathvariant=\"normal\">Ω<!-- Ω --></mml:mi> </mml:math> denotes a bounded open set of <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:mi>N</mml:mi","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66585842","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 : 2023-01-01DOI: 10.14232/ejqtde.2023.1.35
Alexander Grin, Klaus R. Schneider
We consider the Rayleigh equation x ¨ + λ ( x ˙ 2 / 3 − 1 ) x ˙ + x = 0 depending on the real parameter λ and construct a Poincaré–Bendixson annulus A λ in the phase plane containing the unique limit cycle Γ λ of the Rayleigh equation for all λ > 0 . The novelty of this annulus consists in the fact that its boundaries are algebraic curves depending on λ . The polynomial defining the interior boundary represents a special Dulac–Cherkas function for the Rayleigh equation which immediately implies that the Rayleigh equation has at most one limit cycle. The outer boundary is the diffeomorphic image of the corresponding boundary for the van der Pol equation. Additionally we present some equations which are linearly topologically equivalent to the Rayleigh equation and provide also for these equations global algebraic Poincaré–Bendixson annuli.
{"title":"Global algebraic Poincaré–Bendixson annulus for the Rayleigh equation","authors":"Alexander Grin, Klaus R. Schneider","doi":"10.14232/ejqtde.2023.1.35","DOIUrl":"https://doi.org/10.14232/ejqtde.2023.1.35","url":null,"abstract":"We consider the Rayleigh equation x ¨ + λ ( x ˙ 2 / 3 − 1 ) x ˙ + x = 0 depending on the real parameter λ and construct a Poincaré–Bendixson annulus A λ in the phase plane containing the unique limit cycle Γ λ of the Rayleigh equation for all λ > 0 . The novelty of this annulus consists in the fact that its boundaries are algebraic curves depending on λ . The polynomial defining the interior boundary represents a special Dulac–Cherkas function for the Rayleigh equation which immediately implies that the Rayleigh equation has at most one limit cycle. The outer boundary is the diffeomorphic image of the corresponding boundary for the van der Pol equation. Additionally we present some equations which are linearly topologically equivalent to the Rayleigh equation and provide also for these equations global algebraic Poincaré–Bendixson annuli.","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66586101","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 : 2023-01-01DOI: 10.14232/ejqtde.2023.1.5
Equations S. Stević
We present several classes of nonlinear difference equations solvable in closed form, which can be obtained from some known iteration processes, and for some of them we give some generalizations by presenting methods for constructing them. We also conduct several analyses and give many comments related to the difference equations and iteration processes.
{"title":"On some classes of solvable difference equations related to iteration\u0000 processes","authors":"\t\tEquations\t\t\tS. Stević","doi":"10.14232/ejqtde.2023.1.5","DOIUrl":"https://doi.org/10.14232/ejqtde.2023.1.5","url":null,"abstract":"We present several classes of nonlinear difference equations solvable in closed form, which can be obtained from some known iteration processes, and for some of them we give some generalizations by presenting methods for constructing them. We also conduct several analyses and give many comments related to the difference equations and iteration processes.","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":"79 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80907256","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 : 2023-01-01DOI: 10.14232/ejqtde.2023.1.25
Zhengxin Zhou
In this paper, we give the necessary and sufficient conditions for some Ω differential systems to have an analytic commutator, use these properties to judge the origin point of the Ω differential systems to be an isochronous center.
本文给出了一些Ω微分系统具有解析换向子的充要条件，并利用这些性质判断了Ω微分系统的原点是等时中心。
{"title":"On the analytic commutator for Λ−Ω differential systems","authors":"Zhengxin Zhou","doi":"10.14232/ejqtde.2023.1.25","DOIUrl":"https://doi.org/10.14232/ejqtde.2023.1.25","url":null,"abstract":"In this paper, we give the necessary and sufficient conditions for some Ω differential systems to have an analytic commutator, use these properties to judge the origin point of the Ω differential systems to be an isochronous center.","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":"417 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66586515","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 : 2023-01-01DOI: 10.14232/ejqtde.2023.1.43
A. Buică
We add relevant references about which we learned after the completion of the initial work. We mainly show how the concept of exponential trichotomy can successfully replace the one of exponential dichotomy in some results from the paper in the title.
{"title":"Addendum to ``Ulam–Hyers stability and exponentially dichotomic equations in Banach spaces'' [Electron. J. Qual. Theory Differ. Equ. 2023, No. 8, 1–10]","authors":"A. Buică","doi":"10.14232/ejqtde.2023.1.43","DOIUrl":"https://doi.org/10.14232/ejqtde.2023.1.43","url":null,"abstract":"We add relevant references about which we learned after the completion of the initial work. We mainly show how the concept of exponential trichotomy can successfully replace the one of exponential dichotomy in some results from the paper in the title.","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":"86 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66587024","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：