On Positive Solutions for Some Nonlinear Semipositone Elliptic Boundary Value

Abstract

This study concerns the existence of positive solutions to classes of boundary value problems of the form −∆u = g(x,u), x ∈ Ω, u(x) = 0, x ∈ ∂Ω, where ∆ denote the Laplacian operator, Ω is a smooth bounded domain in RN (N ≥ 2) with ∂Ω of class C2, and connected, and g(x, 0) < 0 for some x ∈ Ω (semipositone problems). By using the method of sub-super solutions we prove the existence of positive solution to special types of g(x,u).

Keywords

• positive solutions
• sub-super solution