Multiple positive bound states for critical Schrödinger-Poisson systems

2018/02/07 by Cerami, Giovanna, Molle, Riccardo
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1802.02539

Abstract

Using variational methods we prove some results about existence and multiplicity of positive bound states of to the following Schrödinger-Poisson system: \ \vspace2mm -Δu+V(x)u+K(x)ϕ(x)u=u⁵ -Δϕ=K(x)u² x∈\R³. (SP) We remark that (SP) exhibits a "double" lack of compactness because of the unboundedness of \R³ and the critical growth of the nonlinear term and that in our assumptions ground state solutions of (SP) do not exist.

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