N-Laplacian equations in ℝN with critical growth. (1997)

• Record Type: Journal Article
• Authors: B. do Ó, João Marcos
• Is Part Of: Abstract and applied analysis. Volume 2:Number 3/4(1997)
• Page Start: 301
• Page End: 315
• Publication Date: 1997
• Subjects: Elliptic equations -- p-Laplacian -- critical growth -- Mountain Pass theorem -- Trudinger-Moser inequality; Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/S1085337597000419
• Languages: English
• ISSNs: 1085-3375

Abstract

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 | → ∞ .