{"title":"一类具有广义变号势的Kirchhoff-Choquard方程的存在性和多重性","authors":"E. D. S. Boer, O. Miyagaki, P. Pucci","doi":"10.4171/RLM/984","DOIUrl":null,"url":null,"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.","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2022-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Existence and multiplicity results for a class of Kirchhoff–Choquard equations with a generalized sign-changing potential\",\"authors\":\"E. D. S. Boer, O. Miyagaki, P. Pucci\",\"doi\":\"10.4171/RLM/984\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":54497,\"journal\":{\"name\":\"Rendiconti Lincei-Matematica e Applicazioni\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2022-07-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Rendiconti Lincei-Matematica e Applicazioni\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/RLM/984\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rendiconti Lincei-Matematica e Applicazioni","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/RLM/984","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Existence and multiplicity results for a class of Kirchhoff–Choquard equations with a generalized sign-changing potential
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.
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.