Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 28, pp. 1-14.

Title: Multiple solutions for nonhomogeneous Schrodinger-Poisson system with p-Laplacian
       
Authors: Lanxin Huang (Capital Normal Univ., Beijing, China)
         Jiabao Su (Capital Normal Univ., Beijing, China)

Abstract: 
This article concerns the existence of solutions to the  Schrodinger-Poisson system
$$\displaylines{
-\Delta_p u+|u|^{p-2}u+\lambda\phi u=|u|^{q-2}u+h(x) \quad \text{in }\mathbb{R}^3,\cr
-\Delta \phi=u^2  \quad \text{in }\mathbb{R}^3,
}$$
 where 4/3&lt;p<12/5, p&lt;q&lt;p<sup>*</sup>=3p/(3-p), &Delta;<sub>p</sub> u
=div(|&nabla;u|<sup>p-2</sup>&nabla; u), &lambda;&gt;0, and h not 0.
The multiplicity results are obtained by using  Ekeland's variational principle
and the mountain pass theorem.

Submitted July 8, 2022. Published March 11, 2023.
Math Subject Classifications: 35J10, 35J50, 35J60, 35J92.
Key Words: Nonhomogeneous Schrodinger-Poisson system; variational methods;
           multiple solutions; p-Laplacian.