Positive solutions for nonlinear Schrödinger--Poisson Systems with general nonlinearity

2021/09/05 by Ching‐yu Chen, Chen, Ching-yu, Tsung‐fang Wu +1
Mathematics · #35A15 #35B09 #35J20 #35J61 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2109.02007

openalex publication_date 2021/09/05 · openalex created_date 2022/10/08 · openalex updated_date 2026/07/28

Abstract

In this paper, we study a class of Schrödinger-Poisson (SP) systems with general nonlinearity where the nonlinearity does not require Ambrosetti-Rabinowitz and Nehari monotonic conditions. We establish new estimates and explore the associated energy functional which is coercive and bounded below on Sobolev space. Together with Ekeland variational principle, we prove the existence of ground state solutions. Furthermore, when the `charge' function is greater than a fixed positive number, the (SP) system possesses only zero solutions. In particular, when `charge' function is radially symmetric, we establish the existence of three positive solutions and the symmetry breaking of ground state solutions.

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