Positive and nodal ground state solutions for a critical Schrödinger-Poisson system with indefinite potentials

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Positive and nodal ground state solutions for a critical Schrödinger-Poisson system with indefinite potentials

Furtado, Marcelo F.; Wang, Ying; Zhang, Ziheng

Journal of mathematical analysis and applications, 10/2023, Volume: 526, Issue: 2

Journal Article

We consider the Schrödinger-Poisson system{−Δu+V(x)u+K(x)ϕu=a(x)|u|p−2u+|u|4u,x∈R3,−Δϕ=K(x)u2,x∈R3, where 4<p<6 and the potentials V, a are allowed to change their signs. Under some reasonable assumptions on V, K and a, we apply the constraint minimization argument to establish the existence of positive ground state solutions and ground state nodal solutions.

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Furtado, Marcelo F. | Wang, Ying | Zhang, Ziheng

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