Pub Date : 2023-04-11DOI: 10.1186/s13661-023-01729-y
Zhen Chen, Fan Wu
{"title":"Blow-up criteria of the simplified Ericksen–Leslie system","authors":"Zhen Chen, Fan Wu","doi":"10.1186/s13661-023-01729-y","DOIUrl":"https://doi.org/10.1186/s13661-023-01729-y","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":" ","pages":"1-13"},"PeriodicalIF":1.7,"publicationDate":"2023-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49634195","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 : 2023-04-07DOI: 10.1186/s13661-023-01726-1
E. Alvarez, R. Grau, R. Meriño
Abstract In this paper we investigate the following fractional order in time integrodifferential problem $$ mathbb{D}_{t}^{alpha}u(t)+Au(t)=f bigl(t,u(t) bigr)+ int _{-infty}^{t} k(t-s)g bigl(s,u(s) bigr),ds, quad t in mathbb{R}. $$ Dtαu(t)+Au(t)=f(t,u(t))+∫−∞tk(t−s)g(s,u(s))ds,t∈R. Here, $mathbb{D}_{t}^{alpha}$ Dtα is the Caputo derivative. We obtain results on the existence and uniqueness of $(omega ,c)$ (ω,c) -periodic mild solutions assuming that − A generates an analytic semigroup on a Banach space X and f , g , and k satisfy suitable conditions. Finally, an interesting example that fits our framework is given.
摘要本文研究了时间积分微分问题$$ mathbb{D}_{t}^{alpha}u(t)+Au(t)=f bigl(t,u(t) bigr)+ int _{-infty}^{t} k(t-s)g bigl(s,u(s) bigr),ds, quad t in mathbb{R}. $$ D t α u (t) + A u (t) = f (t, u (t)) +∫−∞t k (t - s) g (s, u (s)) D s, t∈R中的分数阶问题。这里，$mathbb{D}_{t}^{alpha}$ dt α是卡普托导数。假设−A在Banach空间X上生成解析半群，且f、g、k满足适当条件，得到$(omega ,c)$ (ω， c) -周期温和解的存在唯一性。最后，给出了一个适合我们框架的有趣示例。
{"title":"$(omega ,c)$-periodic solutions for a class of fractional integrodifferential equations","authors":"E. Alvarez, R. Grau, R. Meriño","doi":"10.1186/s13661-023-01726-1","DOIUrl":"https://doi.org/10.1186/s13661-023-01726-1","url":null,"abstract":"Abstract In this paper we investigate the following fractional order in time integrodifferential problem $$ mathbb{D}_{t}^{alpha}u(t)+Au(t)=f bigl(t,u(t) bigr)+ int _{-infty}^{t} k(t-s)g bigl(s,u(s) bigr),ds, quad t in mathbb{R}. $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mi>t</mml:mi> <mml:mi>α</mml:mi> </mml:msubsup> <mml:mi>u</mml:mi> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> <mml:mo>+</mml:mo> <mml:mi>A</mml:mi> <mml:mi>u</mml:mi> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>,</mml:mo> <mml:mi>u</mml:mi> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>+</mml:mo> <mml:msubsup> <mml:mo>∫</mml:mo> <mml:mrow> <mml:mo>−</mml:mo> <mml:mi>∞</mml:mi> </mml:mrow> <mml:mi>t</mml:mi> </mml:msubsup> <mml:mi>k</mml:mi> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>−</mml:mo> <mml:mi>s</mml:mi> <mml:mo>)</mml:mo> <mml:mi>g</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>s</mml:mi> <mml:mo>,</mml:mo> <mml:mi>u</mml:mi> <mml:mo>(</mml:mo> <mml:mi>s</mml:mi> <mml:mo>)</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> <mml:mspace /> <mml:mi>d</mml:mi> <mml:mi>s</mml:mi> <mml:mo>,</mml:mo> <mml:mspace /> <mml:mi>t</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>R</mml:mi> <mml:mo>.</mml:mo> </mml:math> Here, $mathbb{D}_{t}^{alpha}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mi>t</mml:mi> <mml:mi>α</mml:mi> </mml:msubsup> </mml:math> is the Caputo derivative. We obtain results on the existence and uniqueness of $(omega ,c)$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>(</mml:mo> <mml:mi>ω</mml:mi> <mml:mo>,</mml:mo> <mml:mi>c</mml:mi> <mml:mo>)</mml:mo> </mml:math> -periodic mild solutions assuming that − A generates an analytic semigroup on a Banach space X and f , g , and k satisfy suitable conditions. Finally, an interesting example that fits our framework is given.","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135742747","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 : 2023-04-05DOI: 10.1186/s13661-023-01725-2
Y. R. S. Leuyacc
{"title":"A class of Schrödinger elliptic equations involving supercritical exponential growth","authors":"Y. R. S. Leuyacc","doi":"10.1186/s13661-023-01725-2","DOIUrl":"https://doi.org/10.1186/s13661-023-01725-2","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":" ","pages":"1-17"},"PeriodicalIF":1.7,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47578184","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 : 2023-04-05DOI: 10.1186/s13661-023-01724-3
M. Ghasemi, Keivan Mohammadi, A. Alipanah
{"title":"Numerical solution of system of second-order integro-differential equations using nonclassical sinc collocation method","authors":"M. Ghasemi, Keivan Mohammadi, A. Alipanah","doi":"10.1186/s13661-023-01724-3","DOIUrl":"https://doi.org/10.1186/s13661-023-01724-3","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":" ","pages":"1-24"},"PeriodicalIF":1.7,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46904030","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 : 2023-04-04DOI: 10.1186/s13661-023-01722-5
Cui Ren, Sen Ming, Xiongmei Fan, Jiayi Du
{"title":"Blow-up of solutions to the semilinear wave equation with scale invariant damping on exterior domain","authors":"Cui Ren, Sen Ming, Xiongmei Fan, Jiayi Du","doi":"10.1186/s13661-023-01722-5","DOIUrl":"https://doi.org/10.1186/s13661-023-01722-5","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":"38 11","pages":"1-25"},"PeriodicalIF":1.7,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41293949","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 : 2023-04-04DOI: 10.1186/s13661-023-01719-0
Changmu Chu, Zhongju He
Abstract In this paper, we study the existence of a class of $p(x)$ p(x) -Kirchhoff equation involving concave-convex nonlinearities. The main tools used are the perturbation technique, variational method, and a priori estimation.
{"title":"Nonnegative nontrivial solutions for a class of $p(x)$-Kirchhoff equation involving concave-convex nonlinearities","authors":"Changmu Chu, Zhongju He","doi":"10.1186/s13661-023-01719-0","DOIUrl":"https://doi.org/10.1186/s13661-023-01719-0","url":null,"abstract":"Abstract In this paper, we study the existence of a class of $p(x)$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>p</mml:mi> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>)</mml:mo> </mml:math> -Kirchhoff equation involving concave-convex nonlinearities. The main tools used are the perturbation technique, variational method, and a priori estimation.","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136188999","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 : 2023-04-01DOI: 10.1186/s13661-023-01717-2
Xingtian Gong, Shuwei Yang
{"title":"A local regularization scheme of Cauchy problem for the Laplace equation on a doubly connected domain","authors":"Xingtian Gong, Shuwei Yang","doi":"10.1186/s13661-023-01717-2","DOIUrl":"https://doi.org/10.1186/s13661-023-01717-2","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":" ","pages":"1-12"},"PeriodicalIF":1.7,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49047211","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 : 2023-03-31DOI: 10.1186/s13661-023-01720-7
Yongxin Jiang, W. Shi, Xiaojuan Li
{"title":"Existence theory for multiple solutions to second-order singular Dirichlet boundary value problem modeling the Antarctic Circumpolar Current","authors":"Yongxin Jiang, W. Shi, Xiaojuan Li","doi":"10.1186/s13661-023-01720-7","DOIUrl":"https://doi.org/10.1186/s13661-023-01720-7","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":"2023 1","pages":"1-19"},"PeriodicalIF":1.7,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43365071","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 : 2023-03-31DOI: 10.1186/s13661-023-01723-4
Baoying Du
Abstract In this paper, we investigate the 3D incompressible Hall-magnetohydrodynamics with partial dissipation. Based on the results in (Du in Bound. Value Probl. 2022:6, 2022; Du and Liu in Acta Math. Sci. 42A:5, 2022; Fei and Xiang in J. Math. Phys. 56:051504, 2015), we establish an improved blow-up criterion for classical solutions. Furthermore, using the blow-up criterion, we also obtain the existence of the classical solutions only under the condition that the initial data $|V_{0}|_{H^{1}}+|B_{0}|_{H^{2}}$ ∥V0∥H1+∥B0∥H2 are sufficiently small.
{"title":"On the blow-up criterion for the Hall-MHD problem with partial dissipation in $mathbb{R}^{3}$","authors":"Baoying Du","doi":"10.1186/s13661-023-01723-4","DOIUrl":"https://doi.org/10.1186/s13661-023-01723-4","url":null,"abstract":"Abstract In this paper, we investigate the 3D incompressible Hall-magnetohydrodynamics with partial dissipation. Based on the results in (Du in Bound. Value Probl. 2022:6, 2022; Du and Liu in Acta Math. Sci. 42A:5, 2022; Fei and Xiang in J. Math. Phys. 56:051504, 2015), we establish an improved blow-up criterion for classical solutions. Furthermore, using the blow-up criterion, we also obtain the existence of the classical solutions only under the condition that the initial data $|V_{0}|_{H^{1}}+|B_{0}|_{H^{2}}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mrow> <mml:mo>∥</mml:mo> <mml:msub> <mml:mi>V</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>∥</mml:mo> </mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:msub> <mml:mo>+</mml:mo> <mml:msub> <mml:mrow> <mml:mo>∥</mml:mo> <mml:msub> <mml:mi>B</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>∥</mml:mo> </mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:msub> </mml:math> are sufficiently small.","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135788031","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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