Physical Sciences and Mathematics Commons^™

Positive Solutions For A Semilinear Elliptic Problem With Critical Exponent, Ismail Ali, Alfonso Castro

All HMC Faculty Publications and Research

No abstract provided in article.

Existence Results For Semipositone Systems, V. Anuradha, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

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.