Two positive solutions to non-autonomous Schrödinger–Poisson systems. (13th September 2019)

• Record Type: Journal Article
• Authors: Sun, Juntao; Wu, Tsung-fang; Feng, Zhaosheng
• Is Part Of: Nonlinearity. Volume 32:Number 10(2019)
• Page Start: 4002
• Page End: 4032
• Publication Date: 2019-09-13
• Subjects: Schrödinger–Poisson system -- variational method -- fibering maps -- Lusternik–Schnirelmann category -- Hilbert manifold; 35J20 -- 35J61 -- 35A01 -- 35B09; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ab289e
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We study the following non-autonomous Schrödinger–Poisson system where 2 < p < 4, and both and are non-negative functions in . By proposing a new analytical method along with the Lusternik–Schnirelmann category, we prove the existence of two bounded positive solutions in, whose energy levels are positive and lie in a definite range. The main feature which distinguishes this paper from other related works lies in the fact that it is the first attempt to study two positive solutions of the above Schrödinger–Poisson system with 2 < p < 4.