Existence and multiplicity of non-trivial solutions for Schrödinger–Kirchhoff-type equations with radial potential

In the present paper, the following Schrödinger–Kirchhoff-type problem equation(P){−(a+b∫RN|∇u|2dx)Δu+V(|x|)u=Q(|x|)f(u),in RN,u(x)→0as |x|→∞, is studied. Four existence theorems of nontrivial solutions and a sequence of high energy solutions for problem (P) are obtained by the Mountain Pass Theorem and symmetric Mountain Pass Theorem.