{"title":"带罗宾边界条件的分数(p_{1}(x,\\cdot )& p_{2}(x,\\cdot ))-拉普拉奇薛定谔型方程的解的存在性和多重性","authors":"Zhenfeng Zhang, Tianqing An, Weichun Bu, Shuai Li","doi":"10.1186/s13661-024-01844-4","DOIUrl":null,"url":null,"abstract":"In this paper, we study fractional $p_{1}(x,\\cdot )\\& p_{2}(x,\\cdot )$ -Laplacian Schrödinger-type equations for Robin boundary conditions. Under some suitable assumptions, we show that two solutions exist using the mountain pass lemma and Ekeland’s variational principle. Then, the existence of infinitely many solutions is derived by applying the fountain theorem and the Krasnoselskii genus theory, respectively. Different from previous results, the topic of this paper is the Robin boundary conditions in $\\mathbb{R}^{N}\\setminus \\overline{\\Omega}$ for fractional order $p_{1}(x,\\cdot )\\& p_{2}(x,\\cdot )$ -Laplacian Schrödinger-type equations, including concave-convex nonlinearities, which has not been studied before. In addition, two examples are given to illustrate our results.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence and multiplicity of solutions for fractional \\\\(p_{1}(x,\\\\cdot )\\\\& p_{2}(x,\\\\cdot )\\\\)-Laplacian Schrödinger-type equations with Robin boundary conditions\",\"authors\":\"Zhenfeng Zhang, Tianqing An, Weichun Bu, Shuai Li\",\"doi\":\"10.1186/s13661-024-01844-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we study fractional $p_{1}(x,\\\\cdot )\\\\& p_{2}(x,\\\\cdot )$ -Laplacian Schrödinger-type equations for Robin boundary conditions. Under some suitable assumptions, we show that two solutions exist using the mountain pass lemma and Ekeland’s variational principle. Then, the existence of infinitely many solutions is derived by applying the fountain theorem and the Krasnoselskii genus theory, respectively. Different from previous results, the topic of this paper is the Robin boundary conditions in $\\\\mathbb{R}^{N}\\\\setminus \\\\overline{\\\\Omega}$ for fractional order $p_{1}(x,\\\\cdot )\\\\& p_{2}(x,\\\\cdot )$ -Laplacian Schrödinger-type equations, including concave-convex nonlinearities, which has not been studied before. In addition, two examples are given to illustrate our results.\",\"PeriodicalId\":49228,\"journal\":{\"name\":\"Boundary Value Problems\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-03-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Boundary Value Problems\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1186/s13661-024-01844-4\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Boundary Value Problems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s13661-024-01844-4","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
Existence and multiplicity of solutions for fractional \(p_{1}(x,\cdot )\& p_{2}(x,\cdot )\)-Laplacian Schrödinger-type equations with Robin boundary conditions
In this paper, we study fractional $p_{1}(x,\cdot )\& p_{2}(x,\cdot )$ -Laplacian Schrödinger-type equations for Robin boundary conditions. Under some suitable assumptions, we show that two solutions exist using the mountain pass lemma and Ekeland’s variational principle. Then, the existence of infinitely many solutions is derived by applying the fountain theorem and the Krasnoselskii genus theory, respectively. Different from previous results, the topic of this paper is the Robin boundary conditions in $\mathbb{R}^{N}\setminus \overline{\Omega}$ for fractional order $p_{1}(x,\cdot )\& p_{2}(x,\cdot )$ -Laplacian Schrödinger-type equations, including concave-convex nonlinearities, which has not been studied before. In addition, two examples are given to illustrate our results.
期刊介绍:
The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.