The effect of diffusions and sources on semilinear elliptic problems

Abstract

This paper deals with properties of non-negative solutions of the boundary value problem in the presence of diffusion a and source f in a bounded domain Ω ⊂ Rn, n ≥ 1, where a and f are non-decreasing continuous functions on [0,L0) and f is positive. Part of the results are new even if we restrict ourselves to the Gelfand type case L0 = ∞, a(t) = t and f is a convex function. We study the behavior of related extremal parameters and solutions with respect to L0 and also to a and f in the C0 topology. The work is carried out in a unified framework for 0 < L0 ≤ ∞ under some interactive conditions between a and f.