Sign-changing solutions for a class of Schrödinger-Bopp-Podolsky system with concave-convex nonlinearities

Abstract

In this article we are devoted to deal with the following Schrödinger-Bopp-Podolsky system{−Δu+V(x)u+ϕu=f(x)|u|q−2u+|u|p−2u,x∈R3,−Δϕ+a2Δ2u=4πu2,x∈R3, where 1<q<2, 4<p<6 and a≥0. Assuming that V(x) satisfies the typically coercive condition and the nonnegative potential f(x) belongs to L66−q(R3) with an appropriate upper bound, we show the existence of sign-changing solutions with positive energy, by means of constraint variational method and quantitative deformation lemma.