Work

Planar Schrödinger-Poisson system with steep potential well: Supercritical exponential case

Year: 2025

Type: article

Abstract: We study a class of planar Schrödinger-Poisson systems$ \left\{ \begin{array}{ll} -\Delta u+\lambda V(x)u+\phi u = f(u), & x\in \mathbb{R}^2, \\ \Delta \phi = u^2, & x\in \mathbb{R}^2, \ \end{array} \right. $where $ \lambda>0 $ is a parameter, $ V\in \mathcal{C}( \mathbb{R}^2, \mathbb{R}^+) $ has a potential well $ \Omega : = \text{int}\, V^{-1}(0) $, and the nonlinearity $ f $ fulfills the supercritical exponential growth at infinity in the Trudinger-Moser sense. By exploiting the mountain-pass theorem and elliptic regularity theory, we establish the existence and concentrating behavior of ground state solutions for sufficiently large $ \lambda $.

Source: Discrete and Continuous Dynamical Systems - S

DOI: 10.3934/dcdss.2025036

Authors: Liejun Shen, Marco Squassina

Institutions: Zhejiang Normal University, Università Cattolica del Sacro Cuore

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Natural Science Foundation of Zhejiang Province

Awards: G4554799872, 平面上临界Choquard方程中的几类变分问题