Existence and multiplicity results for a class of Kirchhoff–Choquard equations with a generalized sign-changing potential

IF 0.6 4区 数学 Q3 MATHEMATICS
E. D. S. Boer, O. Miyagaki, P. Pucci
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引用次数: 5

Abstract

In the present work we are concerned with the following Kirchhoff-Choquard-type equation $$-M(||\nabla u||_{2}^{2})\Delta u +Q(x)u + \mu(V(|\cdot|)\ast u^2)u = f(u) \mbox{ in } \mathbb{R}^2 , $$ for $M: \mathbb{R} \rightarrow \mathbb{R}$ given by $M(t)=a+bt$, $ \mu>0 $, $ V $ a sign-changing and possible unbounded potential, $ Q $ a continuous external potential and a nonlinearity $f$ with exponential critical growth. We prove existence and multiplicity of solutions in the nondegenerate case and guarantee the existence of solutions in the degenerate case.
一类具有广义变号势的Kirchhoff-Choquard方程的存在性和多重性
在本工作中,我们关注以下Kirchhoff-Choquard型方程$$-M(|\nabla u||_{2}^{2})\Delta u+Q(x)u+\mu(V(|\cdot|)\ast u^2)u=f(u)\mbox{In}\mathbb{R}^2,$$for$M:\mathbb{R}\rightarrow\mathbb \R}$由$M(t)=a+bt$给出,$\mu>0$,$V$符号变化和可能的无界势,连续外部势$Q$和指数临界增长的非线性$f$。我们证明了非退化情形下解的存在性和多重性,并保证了退化情形中解的存在。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Rendiconti Lincei-Matematica e Applicazioni
Rendiconti Lincei-Matematica e Applicazioni MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
1.30
自引率
0.00%
发文量
27
审稿时长
>12 weeks
期刊介绍: The journal is dedicated to the publication of high-quality peer-reviewed surveys, research papers and preliminary announcements of important results from all fields of mathematics and its applications.
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