N -Laplacian equations in ℝ N with critical growth

João Marcos B. do Ó

Abstract and Applied Analysis, 1997, vol. 2, 1-15

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 ) , 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 | → ∞ .

Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:464613

DOI: 10.1155/S1085337597000419

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