On the Existence and Stability of Positive Solutions for Some Pairs of Differential Equations (Journal of Partial Differential Equations, 1999)
In this paper, we are concerned with the existence and stability of the positive solutions of a semilinear elliptic system - Δu(x) = a(x)v^6(x) + e(x) - Δv(x) = b(x}u^μ(x) + m(x) \qquad in Ω u = v = 0 \qquad\qquad on ∂Ω where Ω ⊂ R^N is a bounded domain with smooth boundary ∂Ω. It is shown that under the suitable conditions on δ, μ, there exist a stable and an unstable positive solutions for this system if e and m are sufficiently small in L^∞.
Keywords: Positive solutions; multiple solutions; stability; semilincar differential systems