Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 81, pp. 1-17.

Title: Mixed local and nonlocal Schrodinger-Poisson type system involving variable exponents
       
Authors: Xiaolu Lin (Beijing Jiaotong Univ., Beijing, China)
         Shenzhou Zheng (Beijing Jiaotong Univ., Beijing, China)
         
Abstract:  
We consider the existence of solutions for a class of Schrodinger-Poisson type equations
with mixed local and nonlocal p-Laplacian. More precisely, we obtain two distinct
nontrivial solutions for the problem involving variable exponents growth by the
variational methods. Moreover, the phenomena of concentration and multiplicity of
solutions are also investigated as λ→∞.

Submitted May 4, 2022. Published November 28, 2022. 
Math Subject Classifications: 35A15, 35B33, 35R11.
Key Words: Mixed local and nonlocal operator; Schrodinger-Poisson type system;
           multiple solutions; asymptotic behavior; symmetric mountain pass lemma.