We study existence of positive solutions to the coupled-system of boundary value problems of the form
-Δu(x) = λf(x,u,v); x ∈ Ω
-Δv(x) = λg(x,u,v); x ∈ Ω
u(x) = 0 = v(x); x ∈ ∂Ω
where λ > 0 is a parameter, Ω is a bounded domain in R^N; N ≥ 1 with a smooth boundary ∂Ω and f,g are C^1 function with at least one of f(x_0,0,0) or g(x_0,0,0) being negative for some x_0 ∈ Ω (semipositone). We establish our existence results using the method of sub-super solutions. We also discuss non-existence results for λ small.
© 1996 Dynamic Publishers
Anuradha, V., A. Castro and R. Shivaji. “Existence results for semipositone systems”, Journal of Dynamic Systems and Applications, Vol. 5, No. 2, (1996), pp. 219-228.