Boundary Value Problems
Volume 2005 (2005), Issue 3, Pages 323-327
doi:10.1155/BVP.2005.323
Existence of a positive solution for a p-Laplacian semipositone problem
Maya Chhetri1
and R. Shivaji2
1Department of Mathematical Sciences, University of North Carolina at Greensboro, 27402, NC, USA
2Department of Mathematics and Statistics, Mississippi State University, Mississippi State, 39762, MS, USA
Abstract
We consider the boundary value problem −Δpu=λf(u) in Ω satisfying u=0 on ∂Ω, where u=0 on ∂Ω, λ>0 is a parameter, Ω is a bounded domain in ℝn with C2 boundary ∂Ω, and Δpu:=div(|∇u|p−2∇u) for p>1. Here, f:[0,r]→ℝ is a C1 nondecreasing function for some r>0 satisfying f(0)<0 (semipositone). We establish a range of λ for which the above problem has a positive solution when f satisfies certain additional conditions. We employ the method of subsuper solutions to obtain the result.