EXISTENCE OF POSITIVE SOLUTIONS FOR WEAKLY WITH SUPERCRITICAL GROWTH

作者：An, Xiaoming; Deng, Yinbin; Yang, Xian^*

来源：Discrete and Continuous Dynamical Systems-Series S, 2024, 17(2): 801-825.

DOI：10.3934/dcdss.2023096

• Variational methods
• Schrodinger system
• supercritical growth
• positive solutions

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.