Existence and multiplicity of nontrivial solutions for p-Laplacian Schrodinger-Kirchhoff-type equations

In this paper, we are concerned with the following Schrodinger-Kirchhoff-type problem: {-(a + b integral(RN) vertical bar del u vertical bar(p) dx)(p-1) Delta(p)u + lambda V(x)vertical bar u vertical bar(p-2)u = f (x,u), x is an element of R-N, u is an element of W-1,W-p (R-N), (P) where a > 0, b > 0 are constants, Delta(p)u := div(vertical bar del u vertical bar(p-2 del)u) is the p-Laplacian operator with p >= 2, V(x) is the potential function satisfying some conditions which may not guarantee the compactness of the corresponding Sobolev embedding. By using the variational methods, we prove the existence and multiplicity of nontrivial solutions for problem (P). (C) 2015 Elsevier Inc. All rights reserved.