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Topological Methods in Nonlinear Analysis最新文献

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Analyzing multifiltering functions using multiparameter Discrete Morse Theory 用多参数离散莫尔斯理论分析多滤波函数
4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2025-12-11 DOI: 10.12775/tmna.2025.020
Guillaume Brouillette
{"title":"Analyzing multifiltering functions using multiparameter Discrete Morse Theory","authors":"Guillaume Brouillette","doi":"10.12775/tmna.2025.020","DOIUrl":"https://doi.org/10.12775/tmna.2025.020","url":null,"abstract":"A multiparameter filtration, or a multifiltration, may in many cases be seen as the collection of sublevel sets of a vector function, which we call a multifiltering function. The main objective of this paper is to obtain a better understanding of such functions through multiparameter discrete Morse (mdm) theory, which is an extension of Morse-Forman theory to vector-valued functions. Notably, we prove algorithmically that any multifiltering function defined on a simplicial complex can always be approximated by a compatible mdm function. Moreover, we define the Pareto set of a discrete multifiltering function and show that the concept links directly to that of critical simplices of a mdm function. Finally, we experiment with these notions using triangular meshes.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":"1 1","pages":"1-49"},"PeriodicalIF":0.0,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://arxiv.org/pdf/2406.09537","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147884401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Traveling wave solutions in a higher dimensional lattice delayed cooperation system with nonlocal diffusion 具有非局部扩散的高维晶格延迟合作系统的行波解
4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2023-09-30 DOI: 10.12775/tmna.2023.011
Kun Li, Yanli He
{"title":"Traveling wave solutions in a higher dimensional lattice delayed cooperation system with nonlocal diffusion","authors":"Kun Li, Yanli He","doi":"10.12775/tmna.2023.011","DOIUrl":"https://doi.org/10.12775/tmna.2023.011","url":null,"abstract":"This paper is concerned with the existence of traveling wave solutions of a higher dimensional lattice delayed cooperation system with nonlocal diffusion. For sufficiently small intraspecific cooperative delays, we construct upper and lower solutions under two different parameters conditions. And then, by using the monotone iterative and Schauder's fixed point theorem, we obtain the existence of traveling wave solutions. The lower bound of the wave speed is in accordance with the properties of linear determined.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135038943","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
Existence of sign-changing solutions for a third-order boundary value problem with nonlocal conditions of integral type 一类三阶积分型非局部边值问题变符号解的存在性
4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2023-09-23 DOI: 10.12775/tmna.2022.074
Sergey Smirnov
{"title":"Existence of sign-changing solutions for a third-order boundary value problem with nonlocal conditions of integral type","authors":"Sergey Smirnov","doi":"10.12775/tmna.2022.074","DOIUrl":"https://doi.org/10.12775/tmna.2022.074","url":null,"abstract":"We prove the existence of at least one sign-changing solution for a third-order nonlocal boundary value problem by applying Leray-Schauder Continuation Principle. To illustrate the applicability of the obtained results, we consider an example.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135966920","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
On the existence of periodic solutions for Liénard type $phi$-Laplacian equation lisamadard型$ φ $-拉普拉斯方程周期解的存在性
4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2023-09-23 DOI: 10.12775/tmna.2022.067
Congmin Yang, Zaihong Wang
{"title":"On the existence of periodic solutions for Liénard type $phi$-Laplacian equation","authors":"Congmin Yang, Zaihong Wang","doi":"10.12775/tmna.2022.067","DOIUrl":"https://doi.org/10.12775/tmna.2022.067","url":null,"abstract":"In this paper, we study the existence of periodic solutions for a Liénard type $phi$-Laplacian equation $$ (phi(x'))'+f(x)x'+g(x)=p(t). $$ We prove a continuation lemma and use it to prove the existence of periodic solutions for above equation when $g$ or $G$ (the primitive of $g$) satisfies some one-sided or bilateral growth conditions and $F$ (the primitive of $f$) satisfies sublinear condition.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135966113","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
Ground state solution for a class of supercritical Hénon equation with variable exponent 一类变指数超临界hsamnon方程的基态解
4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2023-09-23 DOI: 10.12775/tmna.2022.065
Xiaojing Feng
{"title":"Ground state solution for a class of supercritical Hénon equation with variable exponent","authors":"Xiaojing Feng","doi":"10.12775/tmna.2022.065","DOIUrl":"https://doi.org/10.12775/tmna.2022.065","url":null,"abstract":"This paper is concerned with the following supercritical Hénon equation with variable exponent $$ begin{cases} -Delta u=|x|^{alpha}|u|^{2^*_alpha-2+|x|^beta}u&amp;text{in } B, u=0 &amp;text{on } partial B, end{cases} $$% where $Bsubsetmathbb{R}^N$ $(Ngeq 3)$ is the unit ball, $alpha!> !0$, $ 0!< !beta!< !min{(N!+!alpha)/2,N!-!2}$ and $2^*_alpha=({2N+2alpha})/({N-2})$. We obtain the existence of positive ground state solution by applying the mountain pass theorem, concentration-compactness principle and approximation techniques.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135966913","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
A class of singular $k_i$-Hessian systems 一类奇异k_i -Hessian系统
4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2023-09-23 DOI: 10.12775/tmna.2022.072
Meiqiang Feng
{"title":"A class of singular $k_i$-Hessian systems","authors":"Meiqiang Feng","doi":"10.12775/tmna.2022.072","DOIUrl":"https://doi.org/10.12775/tmna.2022.072","url":null,"abstract":"Our main objective of this article is to investigate a class of singular $k_i$-Hessian systems. Among others, we obtain new theorems on the existence and multiplicity of positive radial solutions. Several nonexistence theorems are also derived.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135966919","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
A planar Schrödinger-Poisson system with vanishing potentials and exponential critical growth 具有消失势和指数临界增长的平面Schrödinger-Poisson系统
4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2023-09-23 DOI: 10.12775/tmna.2022.058
Francisco S. B. Albuquerque, Jonison L. Carvalho, Marcelo F. Furtado, Everaldo S. Medeiros
{"title":"A planar Schrödinger-Poisson system with vanishing potentials and exponential critical growth","authors":"Francisco S. B. Albuquerque, Jonison L. Carvalho, Marcelo F. Furtado, Everaldo S. Medeiros","doi":"10.12775/tmna.2022.058","DOIUrl":"https://doi.org/10.12775/tmna.2022.058","url":null,"abstract":"In this paper we look for ground state solutions of the elliptic system $$ begin{cases} -Delta u+V(x)u+gammaphi K(x)u = Q(x)f(u), &amp;xinmathbb{R}^{2}, Delta phi =K(x) u^{2}, &amp;xinmathbb{R}^{2}, end{cases} $$% where $gamma&gt; 0$ and the continuous potentials $V$, $K$, $Q$ satisfy some mild growth conditions and the nonlinearity $f$ has exponential critical growth. The key point of our approach is a new version of the Trudinger-Moser inequality for weighted Sobolev space.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135966914","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
Injectivity of non-singular planar maps with disconnecting curves in the eigenvalues space 特征值空间中具有断开曲线的非奇异平面映射的注入性
4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2023-09-23 DOI: 10.12775/tmna.2022.073
Marco Sabatini
{"title":"Injectivity of non-singular planar maps with disconnecting curves in the eigenvalues space","authors":"Marco Sabatini","doi":"10.12775/tmna.2022.073","DOIUrl":"https://doi.org/10.12775/tmna.2022.073","url":null,"abstract":"Fessler and Gutierrez cite{Fe}, cite{Gu} proved that if a non-singular planar map has Jacobian matrix without eigenvalues in $(0,+infty)$, then it is injective. We prove that the same holds replacing $(0,+infty)$ with any unbounded curve disconnecting the upper (lower) complex half-plane. Additionally we prove that a Jacobian map $(P,Q)$ is injective if $partial P/partial x + partial Q/partial y$ is not a surjective function.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135966747","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
A note on positive solutions of Lichnerowicz equations involving the $Delta_lambda$-Laplacian 涉及$Delta_lambda$ -拉普拉斯式的Lichnerowicz方程正解的注记
4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2023-09-23 DOI: 10.12775/tmna.2022.076
Anh Tuan Duong, Thi Quynh Nguyen
{"title":"A note on positive solutions of Lichnerowicz equations involving the $Delta_lambda$-Laplacian","authors":"Anh Tuan Duong, Thi Quynh Nguyen","doi":"10.12775/tmna.2022.076","DOIUrl":"https://doi.org/10.12775/tmna.2022.076","url":null,"abstract":"In this paper, we are concerned with the parabolic Lichnerowicz equation involving the $Delta_lambda$-Laplacian $$ v_t-Delta_lambda v=v^{-p-2}-v^p,quad v&gt; 0, quad mbox{ in }mathbb R^Ntimesmathbb R, $$ where $p&gt; 0$ and $Delta_lambda$ is a sub-elliptic operator of the form $$ Delta_lambda=sum_{i=1}^Npartial_{x_i}big(lambda_i^2partial_{x_i}big). $$ Under some general assumptions of $lambda_i$ introduced by A.E. Kogoj and E. Lanconelli in Nonlinear Anal. {bf 75} (2012), no. 12, 4637-4649, we shall prove a uniform lower bound of positive solutions of the equation provided that $p&gt; 0$. Moreover, in the case $p&gt; 1$, we shall show that the equation has only the trivial solution $v=1$. As a consequence, when $v$ is independent of the time variable, we obtain the similar results for the elliptic Lichnerowicz equation involving the $Delta_lambda$-Laplacian $$ -Delta_lambda u=u^{-p-2}-u^p,quad u&gt; 0,quad mbox{in }mathbb R^N. $$","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135966110","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
Three positive solutions for the indefinite fractional Schrödinger-Poisson systems 不定分数阶Schrödinger-Poisson系统的三个正解
4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2023-09-23 DOI: 10.12775/tmna.2022.046
Guofeng Che, Tsung-fang Wu
{"title":"Three positive solutions for the indefinite fractional Schrödinger-Poisson systems","authors":"Guofeng Che, Tsung-fang Wu","doi":"10.12775/tmna.2022.046","DOIUrl":"https://doi.org/10.12775/tmna.2022.046","url":null,"abstract":"In this paper, we are concerned with the following fractionalSchrödinger-Poisson systems with concave-convex nonlinearities: begin{equation*} begin{cases} (-Delta )^{s}u+u+mu l(x)phi u=f(x)|u|^{p-2}u+g(x)|u|^{q-2}u &amp; text{in }mathbb{R}^{3}, (-Delta )^{t}phi =l(x)u^{2} &amp; text{in }mathbb{R}^{3},% end{cases} end{equation*} where ${1}/{2}< tleq s< 1$, $1< q< 2< p< min {4,2_{s}^{ast }}$, $2_{s}^{ast }={6}/({3-2s})$, and $mu > 0$ is a parameter, $fin Cbig(mathbb{R}^{3}big)$ is sign-changing in $mathbb{R}^{3}$ and $gin L^{p/(p-q)}big(mathbb{R}^{3}big)$. Under some suitable assumptions on $l(x)$, $f(x)$ and $g(x)$, we explore that the energy functional corresponding to the system is coercive and bounded below on $H^{alpha }big(mathbb{R}^{3}big)$ which gets a positive solution. Furthermore, we constructed some new estimation techniques, and obtained other two positive solutions. Recent results from the literature are generally improved and extended.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135966748","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
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