부산대학교 도서관

This paper deals with the following perturbed problem with critical exponent (1) − Δ u = u 2 ∗ − 1 + α 2 ∗ u α − 1 v β + ϵ K (x) u p , x ∈ R N , − Δ v = v 2 ∗ − 1 + β 2 ∗ u α v β − 1 + ϵ Q (x) v q , x ∈ R N , u > 0 , v > 0 , x ∈ R N , where 1 ≤ p , q < 2 ∗ − 1 , α + β = 2 ∗ := 2 N N − 2 , α , β ≥ 2 , N = 3, 4 and ε is a parameter. Using a perturbation argument and Lyapunov–Schmidt reduction method, we obtain the existence of positive solutions to problem (1) and the asymptotic property of the solutions. [ABSTRACT FROM AUTHOR]