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Electronic Journal of Qualitative Theory of Differential Equations最新文献

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Properties of Poincaré half-maps for planar linear systems and some direct applications to periodic orbits of piecewise systems 平面线性系统庞卡罗半映射的性质及其在分段系统周期轨道上的直接应用
IF 1.1 4区 数学
Electronic Journal of Qualitative Theory of Differential Equations Pub Date : 2021-09-26 DOI: 10.14232/ejqtde.2023.1.22
V. Carmona, Fernando Fernández-Sánchez, E. García-Medina, D. Novaes
{"title":"Properties of Poincaré half-maps for planar linear systems and some direct applications to periodic orbits of piecewise systems","authors":"V. Carmona, Fernando Fernández-Sánchez, E. García-Medina, D. Novaes","doi":"10.14232/ejqtde.2023.1.22","DOIUrl":"https://doi.org/10.14232/ejqtde.2023.1.22","url":null,"abstract":"This paper deals with fundamental properties of Poincaré half-maps defined on a straight line for planar linear systems. Concretely, we focus on the analyticity of the Poincaré half-maps, their series expansions (Taylor and Newton–Puiseux) at the tangency point and at infinity, the relative position between the graph of Poincaré half-maps and the bisector of the fourth quadrant, and the sign of their second derivatives. All these properties are essential to understand the dynamic behavior of planar piecewise linear systems. Accordingly, we also provide some of their most immediate, but non-trivial, consequences regarding periodic orbits.","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48954527","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}
引用次数: 2
Existence, nonexistence and multiplicity of positive solutions for singular quasilinear problems 奇异拟线性问题正解的存在性、不存在性和多重性
IF 1.1 4区 数学
Electronic Journal of Qualitative Theory of Differential Equations Pub Date : 2021-09-21 DOI: 10.14232/ejqtde.2022.1.13
R. L. Alves
{"title":"Existence, nonexistence and multiplicity of positive solutions for singular quasilinear problems","authors":"R. L. Alves","doi":"10.14232/ejqtde.2022.1.13","DOIUrl":"https://doi.org/10.14232/ejqtde.2022.1.13","url":null,"abstract":"In the present paper we deal with a quasilinear problem involving a singular term and a parametric superlinear perturbation. We are interested in the existence, nonexistence and multiplicity of positive solutions as the parameter \u0000 λ\u0000 >\u0000 0\u0000 varies. In our first result, the superlinear perturbation has an arbitrary growth and we obtain the existence of a solution for the problem by using the sub-supersolution method. For the second result, the superlinear perturbation has subcritical growth and we employ the Mountain Pass Theorem to show the existence of a second solution.","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44110528","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}
引用次数: 0
An extension to the planar Markus–Yamabe Jacobian conjecture 平面Markus-Yamabe雅可比猜想的推广
IF 1.1 4区 数学
Electronic Journal of Qualitative Theory of Differential Equations Pub Date : 2021-06-29 DOI: 10.14232/ejqtde.2021.1.80
Equations M. Sabatini
{"title":"An extension to the planar Markus–Yamabe Jacobian conjecture","authors":"\t\tEquations\t\t\tM. Sabatini","doi":"10.14232/ejqtde.2021.1.80","DOIUrl":"https://doi.org/10.14232/ejqtde.2021.1.80","url":null,"abstract":"We extend the planar Markus–Yamabe Jacobian conjecture to\u0000 differential systems having Jacobian matrix with eigenvalues with negative\u0000 or zero real parts.","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74813894","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}
引用次数: 0
Coupled nonautonomous inclusion systems with spatially variable exponents 具有空间变指数的耦合非自治包涵系统
IF 1.1 4区 数学
Electronic Journal of Qualitative Theory of Differential Equations Pub Date : 2021-01-01 DOI: 10.14232/EJQTDE.2021.1.10
P. Kloeden, J. Simsen
{"title":"Coupled nonautonomous inclusion systems with spatially variable exponents","authors":"P. Kloeden, J. Simsen","doi":"10.14232/EJQTDE.2021.1.10","DOIUrl":"https://doi.org/10.14232/EJQTDE.2021.1.10","url":null,"abstract":"","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66580630","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}
引用次数: 0
Sign-changing solutions for fourth-order elliptic equations of Kirchhoff type with critical exponent 具有临界指数的四阶Kirchhoff型椭圆方程的变符号解
IF 1.1 4区 数学
Electronic Journal of Qualitative Theory of Differential Equations Pub Date : 2021-01-01 DOI: 10.14232/EJQTDE.2021.1.37
Sihua Liang, Binlin Zhang
{"title":"Sign-changing solutions for fourth-order elliptic equations of Kirchhoff type with critical exponent","authors":"Sihua Liang, Binlin Zhang","doi":"10.14232/EJQTDE.2021.1.37","DOIUrl":"https://doi.org/10.14232/EJQTDE.2021.1.37","url":null,"abstract":"","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66581599","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}
引用次数: 1
Differentiability of solutions with respect to parameters in a class of neutral differential equations with state-dependent delays 一类状态相关时滞中立型微分方程解对参数的可微性
IF 1.1 4区 数学
Electronic Journal of Qualitative Theory of Differential Equations Pub Date : 2021-01-01 DOI: 10.14232/ejqtde.2021.1.56
F. Hartung
{"title":"Differentiability of solutions with respect to parameters in a class of neutral differential equations with state-dependent delays","authors":"F. Hartung","doi":"10.14232/ejqtde.2021.1.56","DOIUrl":"https://doi.org/10.14232/ejqtde.2021.1.56","url":null,"abstract":"","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66583106","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}
引用次数: 2
Period function of planar turning points 平面拐点的周期函数
IF 1.1 4区 数学
Electronic Journal of Qualitative Theory of Differential Equations Pub Date : 2021-01-01 DOI: 10.14232/EJQTDE.2021.1.16
R. Huzak, D. Rojas
{"title":"Period function of planar turning points","authors":"R. Huzak, D. Rojas","doi":"10.14232/EJQTDE.2021.1.16","DOIUrl":"https://doi.org/10.14232/EJQTDE.2021.1.16","url":null,"abstract":"This paper is devoted to the study of the period function of planar generic and non-generic turning points. In the generic case (resp. non-generic) a non-degenerate (resp. degenerate) center disappears in the limit e → 0, where e ≥ 0 is the singular perturbation parameter. We show that, for each e > 0 and e ∼ 0, the period function is monotonously increasing (resp. has exactly one minimum). The result is valid in an e-uniform neighborhood of the turning points. We also solve a part of the conjecture about a uniform upper bound for the number of critical periods inside classical Liénard systems of fixed degree, formulated by De Maesschalck and Dumortier in 2007. We use singular perturbation theory and the family blow-up.","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66580778","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}
引用次数: 3
Periodic stationary solutions of the Nagumo lattice differential equation: existence regions and their number Nagumo格微分方程的周期平稳解:存在区域及其数目
IF 1.1 4区 数学
Electronic Journal of Qualitative Theory of Differential Equations Pub Date : 2021-01-01 DOI: 10.14232/EJQTDE.2021.1.23
V. Svígler
{"title":"Periodic stationary solutions of the Nagumo lattice differential equation: existence regions and their number","authors":"V. Svígler","doi":"10.14232/EJQTDE.2021.1.23","DOIUrl":"https://doi.org/10.14232/EJQTDE.2021.1.23","url":null,"abstract":"The Nagumo lattice differential equation admits stationary solutions with arbitrary spatial period for sufficiently small diffusion rate. The continuation from the stationary solutions of the decoupled system (a system of isolated nodes) is used to determine their types; the solutions are labelled by words from a three-letter alphabet. Each stationary solution type can be assigned a parameter region in which the solution can be uniquely identified. Numerous symmetries present in the equation cause some of the regions to have identical or similar shape. With the help of combinatorial enumeration, we derive formulas determining the number of qualitatively different existence regions. We also discuss possible extensions to other systems with more general nonlinear terms and/or spatial structure.","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66580861","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}
引用次数: 2
On solvability of focal boundary value problems for higher order functional differential equations with integral restrictions 带积分限制的高阶泛函微分方程焦点边值问题的可解性
IF 1.1 4区 数学
Electronic Journal of Qualitative Theory of Differential Equations Pub Date : 2021-01-01 DOI: 10.14232/EJQTDE.2021.1.22
E. Bravyi
{"title":"On solvability of focal boundary value problems for higher order functional differential equations with integral restrictions","authors":"E. Bravyi","doi":"10.14232/EJQTDE.2021.1.22","DOIUrl":"https://doi.org/10.14232/EJQTDE.2021.1.22","url":null,"abstract":"","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66581294","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}
引用次数: 0
Analysis of an age-structured dengue model with multiple strains and cross immunity 年龄结构登革热多株交叉免疫模型分析
IF 1.1 4区 数学
Electronic Journal of Qualitative Theory of Differential Equations Pub Date : 2021-01-01 DOI: 10.14232/ejqtde.2021.1.50
Tingting Zheng, L. Nie, Z. Teng, Yantao Luo, Shengfu Wang
{"title":"Analysis of an age-structured dengue model with multiple strains and cross immunity","authors":"Tingting Zheng, L. Nie, Z. Teng, Yantao Luo, Shengfu Wang","doi":"10.14232/ejqtde.2021.1.50","DOIUrl":"https://doi.org/10.14232/ejqtde.2021.1.50","url":null,"abstract":"","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66583030","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}
引用次数: 1
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