EXISTENCE OF SOLUTIONS FOR A CLASS OF P-LAPLACIAN TYPE EQUATION WITH CRITICAL GROWTH AND POTENTIAL VANISHING AT INFINITY

In this paper, we study the existence of positive solution for the following p-Laplacain type equations with critical nonlinearity {-Delta(p)u + V(x)vertical bar u vertical bar(p-2)u = K(x)f(u) + P(x)vertical bar u vertical bar p*(-2)u, x is an element of R-N, u is an element of D-1,D-p(R-N), where Delta(p)u = div(vertical bar del u vertical bar(p-2)del(u)), 1 < p < N, p* = Np/N-p, V(x), K(x) are positive continuous functions which vanish at infinity, f is a function with a subcritical growth, and P(x) is a bounded, nonnegative continuous function. By working in the weighted Sobolev spaces, and using variational method, we prove that the given problem has at least one positive solution.