Infinite Semipositone Problems
by
Jinglong Ye
Mathematics & Statistics Department, Mississippi State University
Coauthors: Eun Kyoung Lee and R. Shivaji

We analyze the positive solutions to singular boundary value problems of the form

-Du = l f(u) ua ; x ∈ W

u = 0;  x ∈ ∂W,

where l is a positive parameter, W is a bounded region in Rⁿ, n ≥ 1 with smooth boundary ∂W, a ∈ (0, 1), D is the Laplacian operator and f is continuous with f(0) < 0. Note that g(s)=[f(s)/(s^a)]→ -∞ as s→ 0⁺ (Infinite Semipositone case). We establish our results by the method of sub-super solution. We also establish extensions to the p-Laplacian case as well as to systems.

PDF

Date received: September 1, 2008