N-Laplacian equations in ℝN with critical growth. (1997) - B. do Ó, João Marcos
Abstract : We study the existence of nontrivial solutions to the following problem:{ u ∈ W 1, N ( ℝ N ), u ≥ 0     and − d i v ( | ∇ u | N − 2 ∇ u ) + a ( x ) | u | N − 2 u = f ( x, u )     in     ℝ N ( N ≥ 2 ), wherea is a continuous function which is coercive, i.e., a ( x ) → ∞   as   | x | → ∞ and the nonlinearityf behaves likeexp ( α | u | N / ( N − 1 ) ) when| u | → ∞ .