Abstract and Applied Analysis
Volume 2 (1997), Issue 3-4, Pages 301-315
doi:10.1155/S1085337597000419
N-Laplacian equations in ℝN with critical growth
Departamento de Matemática, Universidade Federal da Paraíba, João Pessoa 58059.900, Pb, Brazil
Received 10 June 1997
Copyright © 1997 João Marcos B. do Ó. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We study the existence of nontrivial solutions to the following problem: {u∈W1,N(ℝN),u≥0 and−div(|∇u|N−2∇u)+a(x)|u|N−2u=f(x,u) in ℝN(N≥2), where a is a continuous function which is coercive, i.e., a(x)→∞ as |x|→∞
and the nonlinearity f behaves like exp(α|u|N/(N−1)) when |u|→∞.