Ground state sign-changing solutions for a Schrodinger-Poisson system with a 3-linear growth nonlinearity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:455

Article

Zhong, Xiao-Jing^1,2  Tang, Chun-Lei¹ 

[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

[2] Southwest Univ, Sch Hist Culture & Ethnol, Chongqing 400715, Peoples R China

关键词: Schrodinger-Poisson system;    Nonlocal term;    Sign-changing solution;    Ground state;   

DOI  :  10.1016/j.jmaa.2017.04.010

来源: Elsevier

【 摘 要 】

In this paper, we investigate the existence and asymptotic behavior of ground state sign-changing solutions to a class of Schrodinger-Poisson systems {-Delta u + V(x)u + mu phi u = lambda f(x)u + vertical bar u vertical bar(2)u, x is an element of R-3, -Delta phi =u(2), x is an element of R-3, where V is a smooth function, f is nonnegative, mu > 0, lambda < lambda(1) and lambda(1) is the first eigenvalue of the problem -Delta u + V(x)(u) = Delta f(x)(u) in H. With the help of the sign-changing Nehari manifold, we obtain that the Schrodinger Poisson system possesses at least one ground state sign -changing solution u(mu) for all mu > 0 and each lambda < lambda(1). Moreover, we prove that its energy is strictly larger than twice that of ground state solutions. Besides, we give a convergence property of zit, as A SE arrow 0. This paper can be regarded as the complementary work of Shuai and Wang [23], Wang and Zhou [24]. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free