Multiplicity of solutions for a p-Schrodinger-Kirchhoff-type integro-differential equation

We consider the integro-differential problem (P):-(a+b(integral(RN)|del u|(p)dx)(p-1))Delta(u)(p)+V(x)|u|(p-2)u=f(x,u),x is an element of R-N,with|u(x)|--> 0, as|x|-->+infinity. We assume that a, b > 0,N >= 2, 1 < p < N <+infinity,V is an element of C(R-N)with inf(V)> 0, and thatf:R(N)xR--> Rverifies conditionsintroduced by Duan and Huang. We prove the existence of a non-trivial ground statesolution and, by a Ljusternik-Schnirelman scheme, the existence of infinitely manynon-trivial solutions.