{"title":"具有渐近周期项的Schrödinger-Poisson系统解的存在性","authors":"Da-Bin Wang, Lu-Ping Ma, Wen Guan, Hong-Mei Wu","doi":"10.22436/jnsa.011.05.01","DOIUrl":null,"url":null,"abstract":"In this paper, we consider the following nonlinear Schrödinger-Poisson system { −∆u+ V(x)u+K(x)φu = f(x,u), x ∈ R3, −∆φ = K(x)u2, x ∈ R3, where V ,K ∈ L∞(R3) and f : R3 ×R→ R is continuous. We prove that the problem has a nontrivial solution under asymptotically periodic case of V ,K, and f at infinity. Moreover, the nonlinear term f does not satisfy any monotone condition.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"43 1","pages":"591-601"},"PeriodicalIF":0.0000,"publicationDate":"2018-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence of solutions for Schrödinger-Poisson system with asymptotically periodic terms\",\"authors\":\"Da-Bin Wang, Lu-Ping Ma, Wen Guan, Hong-Mei Wu\",\"doi\":\"10.22436/jnsa.011.05.01\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we consider the following nonlinear Schrödinger-Poisson system { −∆u+ V(x)u+K(x)φu = f(x,u), x ∈ R3, −∆φ = K(x)u2, x ∈ R3, where V ,K ∈ L∞(R3) and f : R3 ×R→ R is continuous. We prove that the problem has a nontrivial solution under asymptotically periodic case of V ,K, and f at infinity. Moreover, the nonlinear term f does not satisfy any monotone condition.\",\"PeriodicalId\":22770,\"journal\":{\"name\":\"The Journal of Nonlinear Sciences and Applications\",\"volume\":\"43 1\",\"pages\":\"591-601\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-03-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Journal of Nonlinear Sciences and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22436/jnsa.011.05.01\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Journal of Nonlinear Sciences and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22436/jnsa.011.05.01","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Existence of solutions for Schrödinger-Poisson system with asymptotically periodic terms
In this paper, we consider the following nonlinear Schrödinger-Poisson system { −∆u+ V(x)u+K(x)φu = f(x,u), x ∈ R3, −∆φ = K(x)u2, x ∈ R3, where V ,K ∈ L∞(R3) and f : R3 ×R→ R is continuous. We prove that the problem has a nontrivial solution under asymptotically periodic case of V ,K, and f at infinity. Moreover, the nonlinear term f does not satisfy any monotone condition.
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