Normalized ground state solutions for a class of nonlinear Schrödinger-Poisson equation. (Chinese. English summary) Zbl 07802095

Guo, Shuyan; Guo, Zuji

Acta Math. Appl. Sin. 46, No. 6, 938-951 (2023).

Summary: In this paper, we study the existence of normalized ground state solutions for a class of nonlinear Schrödinger-Poisson equation with parameters. When parameter \(\mu < 0\), by analyzing the structure of Pohozaev manifold and the geometric properties of functional fiber mapping, the method of minimizing sequence and Schwarz radial rearrangement technique are applied to obtain a positive normalized ground state solution of the equation. When the parameter \(\mu > 0\), a (PS) sequence near the Pohozaev manifold is obtained by constructing the auxiliary functional and applying the deformation lemma. Then, the existence of the normalized ground state solution of the equation is obtained by applying the concentration-compactness principle and the monotone method.

MSC:

35J61	Semilinear elliptic equations
35J47	Second-order elliptic systems
35A15	Variational methods applied to PDEs
35B09	Positive solutions to PDEs

Keywords:

Schrödinger-Poisson equation; variational method; normalized solutions; ground state solutions