Electronic Journal of Qualitative Theory of Differential Equations最新文献

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"title":"Ground state solution for fractional problem with critical combined nonlinearities","authors":"Er-Wei Xu, Hong-Rui Sun","doi":"10.14232/ejqtde.2023.1.38","DOIUrl":"https://doi.org/10.14232/ejqtde.2023.1.38","url":null,"abstract":"<jats:p>This paper is concerned with the following nonlocal problem with combined critical nonlinearities <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mo>−<!-- − --></mml:mo> <mml:mi mathvariant=\"normal\">Δ<!-- Δ --></mml:mi> <mml:msup> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>s</mml:mi> </mml:mrow> </mml:msup> <mml:mi>u</mml:mi> <mml:mo>=</mml:mo> <mml:mo>−<!-- − --></mml:mo> <mml:mi>α<!-- α --></mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mi>u</mml:mi> <mml:msup> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>q</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mi>u</mml:mi> <mml:mo>+</mml:mo> <mml:mi>β<!-- β --></mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>u</mml:mi> </mml:mrow> <mml:mo>+</mml:mo> <mml:mi>γ<!-- γ --></mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mi>u</mml:mi> <mml:msup> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:msubsup> <mml:mn>2</mml:mn> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>s</mml:mi> </mml:mrow> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:mrow> </mml:msubsup> <mml:mo>−<!-- − --></mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mi>u</mml:mi> <mml:mspace width=\"1em\" /> <mml:mtext>in</mml:mtext> <mml:mtext> </mml:mtext> <mml:mi mathvariant=\"normal\">Ω<!-- Ω --></mml:mi> <mml:mo>,</mml:mo> <mml:mspace width=\"1em\" /> <mml:mspace width=\"1em\" /> <mml:mi>u</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mspace width=\"1em\" /> <mml:mtext>in</mml:mtext> <mml:mtext> </mml:mtext> <mml:msup> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>N</mml:mi> </mml:mrow> </mml:msup> <mml:mi class=\"MJX-variant\" mathvariant=\"normal\">∖<!-- ∖ --></mml:mi> <mml:mi mathvariant=\"normal\">Ω<!-- Ω --></mml:mi> <mml:mo>,</mml:mo> </mml:math> where <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>s</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=\"false\">)</mml:mo> </mml:math>, <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>N</mml:mi> <mml:mo>></mml:mo> <mml:m","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66586232","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 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":null,"pages":null},"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}

{"title":"Existence and asymptotic behavior of nontrivial solution for Klein–Gordon–Maxwell system with steep potential well","authors":"Xueping Wen, Chunfang Chen","doi":"10.14232/ejqtde.2023.1.17","DOIUrl":"https://doi.org/10.14232/ejqtde.2023.1.17","url":null,"abstract":"<jats:p>In this paper, we consider the following nonlinear Klein–Gordon–Maxwell system with a steep potential well <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:mi mathvariant=\"normal\">Δ<!-- Δ --></mml:mi> <mml:mi>u</mml:mi> <mml:mo>+</mml:mo> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>λ<!-- λ --></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: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>μ<!-- μ --></mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mn>2</mml:mn> <mml:mi>ω<!-- ω --></mml:mi> <mml:mo>+</mml:mo> <mml:mi>ϕ<!-- ϕ --></mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mi>ϕ<!-- ϕ --></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>,</mml:mo> <mml:mi>u</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>,</mml:mo> </mml:mtd> <mml:mtd> <mml:mtext>in</mml:mtext> <mml:mspace width=\"thinmathspace\" /> <mml:msup> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> <mml:mo>,</mml:mo> </mml:mtd> </mml:mtr> <mml:mtr> <mml:mtd> <mml:mi mathvariant=\"normal\">Δ<!-- Δ --></mml:mi> <mml:mi>ϕ<!-- ϕ --></mml:mi> <mml:mo>=</mml:mo> <mml:mi>μ<!-- μ --></mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>ω<!-- ω --></mml:mi> <mml:mo>+</mml:mo> <mml:mi>ϕ<!-- ϕ --></mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:msup> <mml:mi>u</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>,</mml:mo> </mml:mtd> <mml:mtd> <mml:mtext>in</mml:mtext> <mml:mspace width=\"thinmathspace\" /> <mml:msup> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> <mml:mo>,</mml:mo> </mml:mtd> </mml:mtr> </mml:mtable> <mml:mo fence=\"true\" stretchy=\"true\" symmetric=\"true\" /> </mml:mrow> </mml:math> where <mml:m","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66585861","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":"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}