Existence of multiple solutions for modified Schrödinger-Kirchhoff-Poisson type systems via perturbation method with sign-changing potential

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• 作者：Jianhua Chen ^{cjh19881129@163.com} ; Xianhua Tang ; ^{tangxh@mail.csu.edu.cn} ; Zu Gao ^{gaozu7@163.com}
• 关键词：Modified Schrö ; dinger&ndash ; Kirchhoff&ndash ; Poisson system ; Nontrivial nonnegative solutions ; Nontrivial nonpositive solutions ; High energy solutions ; Perturbation methods
• 刊名：Computers & Mathematics with Applications
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：73
• 期：3
• 页码：505-519
• 全文大小：431 K
• 卷排序：73

文摘

In this paper, we prove the existence of positive solutions and negative solutions for the following modified Schrödinger–Kirchhoff–Poisson type systems {−(a+b∫R3∣∇u∣2)Δu+V(x)u+ϕu−12uΔ(u2)=f(x,u),inR3,−Δϕ=u2,inR3, where a>0a>0, b≥0b≥0, VV and ff are continuous functions and V(x)V(x) is allowed to be sign-changing. Under some certain assumptions on VV and ff, we prove the existence of nontrivial nonnegative solutions, nontrivial nonpositive solutions and sequence of high energy solutions via the perturbation method.