N-LAPLACIAN PROBLEMS WITH CRITICAL DOUBLE EXPONENTIAL NONLINEARITIES

In this paper, we prove the existence of a nontrivial solution for the following boundary value problem {-div(omega(x)vertical bar del u(x)vertical bar(N-2)del u(x)) = f (x,u), in B; u = 0, on partial derivative B, where B is the unit ball in R-N, N >= 2, the radial positive weight omega(x) is of logarithmic type, the function f(x, u) is continuous in B x R and has critical double exponential growth, which behaves like exp{e(alpha vertical bar u vertical bar N/N-1)} as vertical bar u vertical bar -> infinity for some alpha > 0.