EXISTENCE OF POSITIVE SOLUTIONS FOR WEAKLY WITH SUPERCRITICAL GROWTH

摘要

This paper focuses on the existence of positive solutions for the following weakly coupled Schro center dot dinger system with supercritical growth except at the origin: @@@ {-Delta u(1) = mu(1)|u(1)|(p(r)-2)u(1) + beta|u(2)|(p(r)/2) |u(1)|(p(r)/2 -)2 u(1), x is an element of B-1(0), @@@ - Delta u(2) = mu(2)|u(2)|(p(r)-2)u(2) + beta|u(1)|(p(r)/2) |u(2)|(p(r)/2-2)u(2), x is an element of B1(0), @@@ where B-1(0) is an unit ball R-N with N >= 3, beta is an element of R is a coupling constant, mu(1), mu(2) is an element of R are constants, p(r) = 2* + r(alpha) with 2* = 2N/N-2 . Assuming that 0 < alpha < min{N/2 , N - 2}, we apply concentration-compactness idea to show that the problem has a positive solution provided that beta > 0 if N >= 5 and beta is an element of (0, beta(0)] boolean OR [beta(1), +infinity) for some positive constants beta(0) < beta(1) if N = 3, 4.

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