Abstract
In this paper we study the existence and multiplicity of positive solutions for the Schrödinger-Poisson system with critical growth:{−ε2Δu+V(x)u=f(u)+|u|3uϕ,x∈R3,−ε2Δϕ=|u|5,x∈R3,u∈H1(R3),u(x)>0,x∈R3, where ε>0 is a parameter, V:R3→R is a continuous function and f:R→R is a C1 function. Under a global condition for V we prove that the above problem has a ground state solution and relate the number of positive solutions with the topology of the set where V attains its minimum, by using variational methods.
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