On a p-Kirchhoff equation via Fountain Theorem and Dual Fountain Theorem

In this paper, we show the existence of infinite solutions to the Kirchhoff type quasilinear elliptic equation [M(integral(Omega)(vertical bar del u vertical bar(p)+lambda(x)vertical bar u vertical bar(p))dx)](p-1) (-Delta(p)u+lambda(x)vertical bar u vertical bar(p-2)u) = f(x, u) in a smooth bounded domain Omega subset of R(N) with nonlinear boundary condition vertical bar del u vertical bar(p-2) partial derivative u/partial derivative v =vertical bar u vertical bar(p-2) on partial derivative Omega. The method we used here is based on "Fountain Theorem" and "Dual Fountain Theorem". (C) 2009 Elsevier Ltd. All rights reserved.