Year: 2025
Author: Lijun Zhu, Hongying Li
Journal of Partial Differential Equations, Vol. 38 (2025), Iss. 1 : pp. 21–33
Abstract
In this paper, we consider the following nonhomogeneous Schrödinger-Poisson system $$\begin{cases}-∆u+u+\eta \phi u=u^5+\lambda f(x), \ & x\in\mathbb{R}^3,\\ -∆\phi=u^2, \ & x\in\mathbb{R}^3, \end{cases}$$where $\eta\ne 0,$ $λ>0$ is a real parameter and $f∈L^{\frac{6}{5}}(\mathbb{R}^3)$ is a nonzero nonnegative function. By using the Mountain Pass theorem and variational method, for $λ$ small, we show that the system with $\eta >0$ has at least two positive solutions, the system with $\eta<0$ has at least one positive solution. Our result generalizes and improves some recent results in the literature.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v38.n1.2
Journal of Partial Differential Equations, Vol. 38 (2025), Iss. 1 : pp. 21–33
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Schrödinger-Poisson system critical exponent variational method positive solutions.