Abstract
In this article, we consider the problem
-Delta u = lambda u(q) + f(1)(u, v) in Omega
-Delta v = lambda v(q) + f(2)(u, v) in Omega
u, v > 0 in Omega u = v = 0 on partial derivative Omega,
where Omega is a bounded domain in R-2, 0 < q < 1, and lambda > 0. We show that there exists a real number Lambda such that the above problem admits at least two solutions for lambda is an element of (0, Lambda), and no solution for lambda > Lambda.