Electronic Journal of Qualitative Theory of Differential Equations最新文献

{"title":"Concentration of solutions for ( N , q )-Laplacian equatio","authors":"L. Wang, Jun Wang, Binlin Zhang","doi":"10.14232/ejqtde.2023.1.14","DOIUrl":"https://doi.org/10.14232/ejqtde.2023.1.14","url":null,"abstract":"<jats:p>In this article, we consider the concentration of positive solutions for the following equation with Trudinger–Moser nonlinearity: <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>N</mml:mi> </mml:msub> <mml:mi>u</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:msub> <mml:mi mathvariant=\"normal\">Δ<!-- Δ --></mml:mi> <mml:mi>q</mml:mi> </mml:msub> <mml:mi>u</mml:mi> <mml:mo>+</mml:mo> <mml:mi>V</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>ε<!-- ε --></mml:mi> <mml:mi>x</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo stretchy=\"false\">(</mml:mo> <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>N</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: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 stretchy=\"false\">)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>f</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>u</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>,</mml:mo> </mml:mtd> <mml:mtd> <mml:mi>x</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <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:mo>,</mml:mo> </mml:mtd> </mml:mtr> <mml:mtr> <mml:mtd> <mml:mi>u</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:msup> <mml:mi>W</mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> ","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":"66585399","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":"Homoclinic solutions for a class of asymptotically autonomous Hamiltonian systems with indefinite sign nonlinearities","authors":"Donglun Wu","doi":"10.14232/ejqtde.2023.1.31","DOIUrl":"https://doi.org/10.14232/ejqtde.2023.1.31","url":null,"abstract":"In this paper, we obtain the multiplicity of homoclinic solutions for a class of asymptotically autonomous Hamiltonian systems with indefinite sign potentials. The concentration-compactness principle is applied to show the compactness. As a byproduct, we obtain the uniqueness of the positive ground state solution for a class of autonomous Hamiltonian systems and the best constant for Sobolev inequality which are of independent interests.","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":"66586370","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":"The family of cubic differential systems with two real and two complex distinct infinite singularities and invariant straight lines of the type ( 3","authors":"Cristina Bujac, D. Schlomiuk, N. Vulpe","doi":"10.14232/ejqtde.2023.1.40","DOIUrl":"https://doi.org/10.14232/ejqtde.2023.1.40","url":null,"abstract":"In this article we consider the class CSL 7 2 r 2 c ∞ of non-degenerate real planar cubic vector fields, which possess two real and two complex distinct infinite singularities and invariant straight lines of total multiplicity 7, including the line at infinity. The classification according to the configurations of invariant lines of systems possessing invariant straight lines was given in articles published from 2014 up to 2022. We continue our investigation for the family CSL 7 2 r 2 c ∞ possessing configurations of invariant lines of type ( 3 , 1 , 1 , 1 ) and prove that there are exactly 42 distinct configurations of this type. Moreover we construct all the orbit representatives of the systems in this class with respect to affine group of transformations and a time rescaling.","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":"66586819","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":"Qualitative analysis on the diffusive Holling–Tanner predator–prey model","authors":"Xu Zhao, Wenshu Zhou","doi":"10.14232/ejqtde.2023.1.41","DOIUrl":"https://doi.org/10.14232/ejqtde.2023.1.41","url":null,"abstract":"We consider the diffusive Holling–Tanner predator–prey model subject to the homogeneous Neumann boundary condition. We first apply Lyapunov function method to prove some global stability results of the unique positive constant steady-state. And then, we derive a non-existence result of positive non-constant steady-states by a novel approach that can also be applied to the classical Sel'kov model to obtain the non-existence of positive non-constant steady-states if 0 < p ≤ 1 .","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":"66586862","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":"The logistic equation in the context of Stieltjes differential and\u0000 integral equations","authors":"\t\tEquations\t\t\tIgnacio Márquez Albés, A. Slavík","doi":"10.14232/ejqtde.2023.1.10","DOIUrl":"https://doi.org/10.14232/ejqtde.2023.1.10","url":null,"abstract":"In this paper, we introduce logistic equations with Stieltjes derivatives and provide explicit solution formulas. As an application, we present a population model which involves intraspecific competition, periods of hibernation, as well as seasonal reproductive cycles. We also deal with various forms of Stieltjes integral equations, and find the corresponding logistic equations. We show that our work extends earlier results for dynamic equations on time scales, which served as an inspiration for this paper.","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":"150 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79483851","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 solution of a bioeconomic fishery model by coincidence degree theory","authors":"S. Srivastava, S. Padhi, A. Domoshnitsky","doi":"10.14232/ejqtde.2023.1.29","DOIUrl":"https://doi.org/10.14232/ejqtde.2023.1.29","url":null,"abstract":"&lt;jats:p&gt;In this article we use coincidence degree theory to study the existence of a positive periodic solutions to the following bioeconomic model in fishery dynamics &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;{&lt;/mml:mo&gt; &lt;mml:mtable columnalign=\"left left\" rowspacing=\".2em\" columnspacing=\"1em\" displaystyle=\"false\"&gt; &lt;mml:mtr&gt; &lt;mml:mtd&gt; &lt;mml:mfrac&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;d&lt;/mml:mi&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;d&lt;/mml:mi&gt; &lt;mml:mi&gt;t&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:mfrac&gt; &lt;mml:mo&gt;=&lt;/mml:mo&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;(&lt;/mml:mo&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;r&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;t&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;(&lt;/mml:mo&gt; &lt;mml:mrow&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;mml:mo&gt;−&lt;!-- − --&gt;&lt;/mml:mo&gt; &lt;mml:mfrac&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;mml:mi&gt;K&lt;/mml:mi&gt; &lt;/mml:mfrac&gt; &lt;/mml:mrow&gt; &lt;mml:mo&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:mo&gt;−&lt;!-- − --&gt;&lt;/mml:mo&gt; &lt;mml:mfrac&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;q&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;t&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;mml:mi&gt;E&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;mml:mo&gt;+&lt;/mml:mo&gt; &lt;mml:mi&gt;D&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:mfrac&gt; &lt;/mml:mrow&gt; &lt;mml:mo&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;/mml:mtd&gt; &lt;/mml:mtr&gt; &lt;mml:mtr&gt; &lt;mml:mtd&gt; &lt;mml:mfrac&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;d&lt;/mml:mi&gt; &lt;mml:mi&gt;E&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;d&lt;/mml:mi&gt; &lt;mml:mi&gt;t&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:mfrac&gt; &lt;mml:mo&gt;=&lt;/mml:mo&gt; &lt;mml:mi&gt;E&lt;/mml:mi&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;(&lt;/mml:mo&gt; &lt;mml:mrow&gt; &lt;mml:mfrac&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;A&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;t&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;mml:mi&gt;q&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;t&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; ","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":"66586284","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":" 1 / 2 -Laplacian problem with logarithmic and exponential nonlinearities","authors":"Zigao Chen","doi":"10.14232/ejqtde.2023.1.37","DOIUrl":"https://doi.org/10.14232/ejqtde.2023.1.37","url":null,"abstract":"In this paper, based on a suitable fractional Trudinger–Moser inequality, we establish sufficient conditions for the existence result of least energy sign-changing solution for a class of one-dimensional nonlocal equations involving logarithmic and exponential nonlinearities. By using a main tool of constrained minimization in Nehari manifold and a quantitative deformation lemma, we consider both subcritical and critical exponential growths. This work can be regarded as the complement for some results of the literature.","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135310985","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 perturbations of reducible scalar second order functional differential equations","authors":"A. Calamai, M. Pera, M. Spadini","doi":"10.14232/ejqtde.2023.1.18","DOIUrl":"https://doi.org/10.14232/ejqtde.2023.1.18","url":null,"abstract":"Using a topological approach we investigate the structure of the set of forced oscillations of a class of reducible second order functional retarded differential equations subject to periodic forcing. More precisely, we consider a delay-type functional dependence involving a gamma probability distribution and, using a linear chain trick, we formulate a first order system of ODEs whose T -periodic solutions correspond to those of the functional equation.","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":"66585965","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":"Qualitative analysis of a mechanical system of coupled nonlinear oscillators","authors":"G. Moroşanu, C. Vladimirescu","doi":"10.14232/ejqtde.2023.1.16","DOIUrl":"https://doi.org/10.14232/ejqtde.2023.1.16","url":null,"abstract":"In this paper we investigate nonlinear systems of second order ODEs describing the dynamics of two coupled nonlinear oscillators of a mechanical system. We obtain, under certain assumptions, some stability results for the null solution. Also, we show that in the presence of a time-dependent external force, every solution starting from sufficiently small initial data and its derivative are bounded or go to zero as the time tends to + ∞ , provided that suitable conditions are satisfied. Our theoretical results are illustrated with numerical simulations.","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":"66585734","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":"Bifurcations and Turing patterns in a diffusive Gierer–Meinhardt model","authors":"Yong Wang, Mengping Guo, Weihua Jiang","doi":"10.14232/ejqtde.2023.1.27","DOIUrl":"https://doi.org/10.14232/ejqtde.2023.1.27","url":null,"abstract":"In this paper, the Hopf bifurcations and Turing bifurcations of the Gierer–Meinhardt activator-inhibitor model are studied. The very interesting and complex spatially periodic solutions and patterns induced by bifurcations are analyzed from both theoretical and numerical aspects respectively. Firstly, the conditions for the existence of Hopf bifurcation and Turing bifurcation are established in turn. Then, the Turing instability region caused by diffusion is obtained. In addition, to uncover the diffusion mechanics of Turing patterns, the dynamic behaviors are studied near the Turing bifurcation by using weakly nonlinear analysis techniques, and the type of spatial pattern was predicted by the amplitude equation. And our results show that the spatial patterns in the Turing instability region change from the spot, spot-stripe to stripe in order. Finally, the results of the analysis are verified by numerical simulations.","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":"66586156","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}