ON THE DIRICHLET PROBLEM FOR THE GENERALIZED n-LAPLACIAN: SINGULAR NONLINEARITY WITH THE EXPONENTIAL AND MULTIPLE EXPONENTIAL CRITICAL GROWTH RANGE
2013
Abstrakt
Let Omega subset of R-n, n >= 2, be a bounded domain containing the origin. Applying the Mountain Pass Theorem and a singular version of the generalized Moser-Trudinger inequality we prove the existence of a non-trivial weak solution to the problem u is an element of(W0L Phi)-L-1(Omega) and -div(Phi'(vertical bar del u vertical bar)del u/vertical bar del u vertical bar = f(x,u)/vertical bar x vertical bar(a) in Omega, where a subset of [0,n), Phi is a Young function such that the space (W0L)-L-1 Phi(Omega) is embedded into exponential or multiple exponential Orlicz space and f (x,t) has the corresponding critical growth.