Solutions with prescribed mass for the p-Laplacian Schrödinger-Poisson system with critical growth

Abstract

In this paper, we focus on the existence and multiplicity of solutions for the p-Laplacian Schrödinger-Poisson system {pu+|u|p2u=|u|p2u+|u|q2u+|u|pu,inR3,=|u|p,inR3, with a prescribed mass given by R3|u|pdx=ap, in the Sobolev critical case, where, 1<p<3,a>0, and >0, >0 are parameters, [Formula presented] is the Sobolev critical exponent, and R is an undetermined parameter, acting as a Lagrange multiplier. We investigate this system under the Lp-subcritical perturbation |u|q2u, with [Formula presented], and establish the existence of multiple normalized solutions using the truncation technique, concentration-compactness principle, and genus theory. In the Lp-supercritical regime: [Formula presented], we prove two existence results for normalized solutions under different assumptions for the parameters ,, by employing the Pohozaev manifold analysis, concentration-compactness principle and mountain pass theorem. This study presents new contributions regarding the existence and multiplicity of normalized solutions of the p-Laplacian critical Schrödinger-Poisson problem, perturbed with a subcritical term in the whole space R3, for the first time.

In this paper, we focus on the existence and multiplicity of solutions for the p-Laplacian Schrödinger-Poisson system {pu+|u|p2u=|u|p2u+|u|q2u+|u|pu,inR3,=|u|p,inR3, with a prescribed mass given by R3|u|pdx=ap, in the Sobolev critical case, where, 1<p<3,a>0, and >0, >0 are parameters, [Formula presented] is the Sobolev critical exponent, and R is an undetermined parameter, acting as a Lagrange multiplier. We investigate this system under the Lp-subcritical perturbation |u|q2u, with [Formula presented], and establish the existence of multiple normalized solutions using the truncation technique, concentration-compactness principle, and genus theory. In the Lp-supercritical regime: [Formula presented], we prove two existence results for normalized solutions under different assumptions for the parameters ,, by employing the Pohozaev manifold analysis, concentration-compactness principle and mountain pass theorem. This study presents new contributions regarding the existence and multiplicity of normalized solutions of the p-Laplacian critical Schrödinger-Poisson problem, perturbed with a subcritical term in the whole space R3, for the first time.