Existence of least-energy sign-changing solutions for Schrodinger-Poisson system with critical growth

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:479

Article

Wang, Da-Bin¹  Zhang, Hua-Bo¹  Guan, Wen¹ 

[1] Lanzhou Univ Technol, Dept Appl Math, Lanzhou 730050, Gansu, Peoples R China

关键词: Schrodinger-Poisson system;    Nonlocal term;    Variation methods;    Sign-changing solutions;   

DOI  :  10.1016/j.jmaa.2019.07.052

来源: Elsevier

【 摘 要 】

In this paper, we study the following Schrodinger-Poisson system {-Delta u + V(x)u + lambda phi u = vertical bar u vertical bar(4)u + mu f(u), x is an element of R-3, -Delta phi = u(2), x is an element of R-3, where V(x) is a smooth function and mu, lambda > 0. Under suitable conditions on f, by using constraint variational method and the quantitative deformation lemma, if mu is large enough, we obtain a least-energy sign-changing (or nodal) solution u(lambda) to this problem for each lambda > 0, and its energy is strictly larger than twice that of the ground state solutions. Moreover, we study the asymptotic behavior of u(lambda), as the parameter lambda SE arrow 0. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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