Existence of a positive solution for a p-Laplacian semipositone problem. (13th November 2005) - Chhetri, Maya; Shivaji, R.
Abstract : We consider the boundary value problem− Δ p u = λ f ( u ) inΩ satisfyingu = 0 on∂ Ω, whereu = 0 on∂ Ω, λ > 0 is a parameter, Ω is a bounded domain inℝ n withC 2 boundary∂ Ω, andΔ p u : = div ( | ∇ u | p − 2 ∇ u ) forp > 1 . Here, f : [ 0, r ] → ℝ is aC 1 nondecreasing function for somer > 0 satisfyingf ( 0 ) < 0 (semipositone). We establish a range ofλ for which the above problem has a positive solution whenf satisfies certain additional conditions. We employ the method of subsuper solutions to obtain the result.