Existence, non-existence and degeneracy of limit solutions to p-Laplace problems involving Hardy potentials as p1^+. The case of a critical drift

In this paper we analyze the asymptotic behaviour as p 1^+ of solutions uₚ to \ array{rclr -ₚu&=&| u|^p-2 u|x|²+ f& in, \\ uₚ&=&0 & on, array. where is a bounded open subset of RN with Lipschitz boundary containing the origin, , and f is a nonnegative datum in L^N, (). As a consequence, under suitable smallness assumptions on f and, we show sharp existence results of bounded solutions to the Dirichlet problems cases - ₁ u = u|D u| x|x|²+f & in\, , u=0 & on\, cases where ₁u=div\, (Du|Du|) is the 1-Laplacian operator. The case of a generic drift term in L^N, () is also considered. Explicits examples are given in order to show the optimality of the main assumptions on the data.