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

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

Článek WoS

In this paper, we focus on the existence and multiplicity of solutions for the p-Laplacian Schrödinger-Poisson system {−Δpu+γϕ|u|p−2u=λ|u|p−2u+μ|u|q−2u+|u|pu,inR3,−Δϕ=|u|p,inR3, with a prescribed mass given by ∫R3|u|pdx=ap, in the Sobolev critical case, where, 10, and γ>0, μ>0 are parameters, [Formula presented] is the Sobolev critical exponent, and λ∈R is an undetermined parameter, acting as a Lagrange multiplier. We investigate this system under the Lp-subcritical perturbation μ|u|q−2u, 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 γ,μ, 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 {−Δpu+γϕ|u|p−2u=λ|u|p−2u+μ|u|q−2u+|u|pu,inR3,−Δϕ=|u|p,inR3, with a prescribed mass given by ∫R3|u|pdx=ap, in the Sobolev critical case, where, 10, and γ>0, μ>0 are parameters, [Formula presented] is the Sobolev critical exponent, and λ∈R is an undetermined parameter, acting as a Lagrange multiplier. We investigate this system under the Lp-subcritical perturbation μ|u|q−2u, 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 γ,μ, 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.

Concentration-compactness principle; Genus theory; Normalized solutions; p-Laplacian Schrödinger-Poisson system; Sobolev critical exponent

Concentration-compactness principle; Genus theory; Normalized solutions; p-Laplacian Schrödinger-Poisson system; Sobolev critical exponent

LIU, K.; HE, X.; RADULESCU, V.

25.10.2025

Elsevier

1090-2732

Journal of Differential Equations

443

11

Spojené státy americké

1

51

51

https://www.sciencedirect.com/science/article/pii/S0022039625005972

http://hdl.handle.net/11012/255463