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Existence of solutions for perturbed elliptic system with critical exponents (2015)

Juan Jiang; Wenbin Liu

Springer

In: Boundary Value Problems

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Publication Date: 2015-06-12

Description: In this paper, the perturbed elliptic system with critical exponents − ε 2 Δ u + V ( x ) u = f ( x , u ) + α α + β K ( x ) | u | α − 2 u | v | β , x ∈ R N , − ε 2 Δ v + V ( x ) v = g ( x , v ) + β α + β K ( x ) | u | α | v | β − 2 v , x ∈ R N , is considered, where α 〉 1 , β 〉 1 satisfy α + β = 2 ∗ , and 2 ∗ = 2 N / ( N − 2 ) ( N ≥ 3 ) is the Sobolev critical exponent. Under proper conditions on V, f, g, and K, the existence result is obtained by using variational methods.MSC: 35B33, 35J60, 35J65.

Print ISSN: 1687-2762

Electronic ISSN: 1687-2770

Topics: Mathematics

Published by Springer

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