Electronic Journal of Qualitative Theory of Differential Equations最新文献

{"title":"Weighted L p -type regularity estimates for nonlinear parabolic equations with Orlicz growth","authors":"F. Yao","doi":"10.14232/ejqtde.2022.1.17","DOIUrl":"https://doi.org/10.14232/ejqtde.2022.1.17","url":null,"abstract":"<jats:p>In this paper we obtain the following weighted <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> </mml:math>-type regularity estimates <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"> <mml:mi>B</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow> <mml:mo>|</mml:mo> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi mathvariant=\"bold\">f</mml:mi> </mml:mrow> <mml:mo>|</mml:mo> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:msup> <mml:mi>L</mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>q</mml:mi> </mml:mrow> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow> <mml:mi>ν<!-- ν --></mml:mi> <mml:mo>,</mml:mo> <mml:mi>ν<!-- ν --></mml:mi> <mml:mo>+</mml:mo> <mml:mi>T</mml:mi> <mml:mo>;</mml:mo> <mml:msubsup> <mml:mi>L</mml:mi> <mml:mi>w</mml:mi> <mml:mi>q</mml:mi> </mml:msubsup> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi mathvariant=\"normal\">Ω<!-- Ω --></mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> <mml:mtext> </mml:mtext> <mml:mstyle displaystyle=\"false\" scriptlevel=\"0\"> <mml:mtext>locally</mml:mtext> </mml:mstyle> <mml:mo stretchy=\"false\">⇒<!-- ⇒ --></mml:mo> <mml:mi>B</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow> <mml:mo>|</mml:mo> <mml:mrow> <mml:mi mathvariant=\"normal\">∇<!-- ∇ --></mml:mi> <mml:mi>u</mml:mi> </mml:mrow> <mml:mo>|</mml:mo> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:msup> <mml:mi>L</mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>q</mml:mi> </mml:mrow> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow> <mml:mi>ν<!-- ν --></mml:mi> <mml:mo>,</mml:mo> <mml:mi>ν<!-- ν --></mml:mi> <mml:mo>+</mml:mo> <mml:mi>T</mml:mi> <mml:mo>;</mml:mo> <mml:msubsup> <mml:mi>L</mml:mi> <mml:mi>w</mml:mi> <mml:mi>q</mml:mi> </mml:msubsup> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi mathvariant=\"normal\">Ω<!-- Ω --></mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> <mml:mtext> </mml:mtext> <mml:mstyle displaystyle=\"false\" scriptlevel=\"0\"> <mml:mtext>locally</mml:mtext> </mml:mstyle> </mml:math> for any <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>q</mml:mi> <mml:mo>></mml:mo> <mml:mn>1</mml:mn> </mml:math> of weak solutions for non-homogeneous nonlinear parabolic equations with Orlicz growth <mml:math xmlns:mml=\"http://www.w3.org/1998","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":"66583631","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}

{"title":"Solvability of thirty-six three-dimensional systems of difference equations of hyperbolic-cotangent type","authors":"S. Stević","doi":"10.14232/ejqtde.2022.1.26","DOIUrl":"https://doi.org/10.14232/ejqtde.2022.1.26","url":null,"abstract":"We present thirty-six classes of three-dimensional systems of difference equations of the hyperbolic-cotangent type which are solvable in closed form.","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":"66584116","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}

{"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}

{"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}

{"title":"Multi-bump solutions for the magnetic Schrödinger–Poisson system with critical growth","authors":"Chao Ji, YongDe Zhang, V. Rǎdulescu","doi":"10.14232/ejqtde.2022.1.21","DOIUrl":"https://doi.org/10.14232/ejqtde.2022.1.21","url":null,"abstract":"<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> ","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":"66584483","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}

{"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}

{"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}

{"title":"Existence and multiplicity of eigenvalues for some double-phase problems involving an indefinite sign reaction term","authors":"Vasile-Florin Uţă","doi":"10.14232/ejqtde.2022.1.5","DOIUrl":"https://doi.org/10.14232/ejqtde.2022.1.5","url":null,"abstract":"<jats:p>We study the following class of double-phase nonlinear eigenvalue problems <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>−<!-- − --></mml:mo> <mml:mi>div</mml:mi> <mml:mo>⁡<!-- ⁡ --></mml:mo> <mml:mrow> <mml:mo>[</mml:mo> <mml:mrow> <mml:mi>ϕ<!-- ϕ --></mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mi mathvariant=\"normal\">∇<!-- ∇ --></mml:mi> <mml:mi>u</mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mi mathvariant=\"normal\">∇<!-- ∇ --></mml:mi> <mml:mi>u</mml:mi> <mml:mo>+</mml:mo> <mml:mi>ψ<!-- ψ --></mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mi mathvariant=\"normal\">∇<!-- ∇ --></mml:mi> <mml:mi>u</mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mi mathvariant=\"normal\">∇<!-- ∇ --></mml:mi> <mml:mi>u</mml:mi> </mml:mrow> <mml:mo>]</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mi>λ<!-- λ --></mml:mi> <mml:mi>f</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:mi>u</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:math> in <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi mathvariant=\"normal\">Ω<!-- Ω --></mml:mi> </mml:math>, <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>u</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:math> on <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi mathvariant=\"normal\">∂<!-- ∂ --></mml:mi> <mml:mi mathvariant=\"normal\">Ω<!-- Ω --></mml:mi> </mml:math>, where <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi mathvariant=\"normal\">Ω<!-- Ω --></mml:mi> </mml:math> is a bounded domain from <mml:math xmlns:mml=\"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> </mml:msup> </mml:math> and the potential functions <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>ϕ<!-- ϕ --></mml:mi> </mml:math> and <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>ψ<!-- ψ --></mml:mi> </mml:math> have <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo stretchy=\"false\">(</mml:mo> <mml:msub> <mml:mi>p</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>;</mml:mo> <mml","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":"66585217","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}

{"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}

{"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}