Abstract
This article concerns the existence and the nonexistence of solution for the following boundary problem involving the p-biharmonic operator and singular nonlinearities, Delta(2)(p)u = vertical bar u vertical bar gamma(-1)u + mu(vertical bar u vertical bar(-1-alpha)/vertical bar x vertical bar beta)u in O and u = partial derivative u/partial derivative n = 0 on partial derivative Omega, where 4 < 2p < N, 0 is an element of Omega, -infinity < mu < mu(*), = (N - 2p)(1 - alpha)/pN, p < gamma < p* = pN/N - 2p is the critical Sobolev exponent, 0 <= beta < N (gamma + alpha)/(gamma + 1), 0 < alpha < 1. Under some sufficient conditions on coefficients, we prove the existence of at least one nontrivial solutions in E by using variational methods. By using the Pohozaev identity type, we show the nonexistence of positive solution when Omega subset of R-N be a bounded, smoothandstrictlystar-shapeddomain, beta = 0 and gamma >= gamma(*), = pN(1 - alpha)/(N - 2p)(1 - alpha) - mu Np > p* = pN/N - 2p.