Existence of positive solutions for a class of nonlocal elliptic systems with multiple parameters

摘要

In this paper, we study the existence of positive solutions to the following nonlocal elliptic systems . . . . . .M 1 . | u| p dx . p u = α 1 a(x)f 1 (v) + β 1 b(x)g 1 (u), x ∈ ., .M 2 . | v| q dx . q v = α 2 c(x)f 2 (u) + β 2 d(x)g 2 (v ), x ∈ ., u = v = 0, x ∈ .., where . is a bounded domain in R N with smooth boundary .., 1 < p, q < N, M i : R + 0 → R , i = 1, 2, are continuous and nondecreasing functions, a, b, c, d ∈ C( .), and α i , β i , i = 1, 2, are positive parameters.