Existence and asymptotic behavior of solutions for nonlinear Schrödinger-Poisson systems with steep potential well

Miao Du; Lixin Tian; Jun Wang; Fubao Zhang

doi:10.1063/1.4941036

Existence and asymptotic behavior of solutions for nonlinear Schrödinger-Poisson systems with steep potential well

J Math Phys. 2016 Mar;57(3):031502. doi: 10.1063/1.4941036. Epub 2016 Mar 7.

Authors

Miao Du¹, Lixin Tian¹, Jun Wang², Fubao Zhang³

Affiliations

¹ School of Mathematical Sciences, Nanjing Normal University , Nanjing 210023, People's Republic of China.
² Faculty of Science, Jiangsu University , Zhenjiang 212013, People's Republic of China.
³ Department of Mathematics, Southeast University , Nanjing 210096, People's Republic of China.

Abstract

In this paper, we are concerned with a class of Schrödinger-Poisson systems with the asymptotically linear or asymptotically 3-linear nonlinearity. Under some suitable assumptions on V, K, a, and f, we prove the existence, nonexistence, and asymptotic behavior of solutions via variational methods. In particular, the potential V is allowed to be sign-changing for the asymptotically linear case.