Existence of a positive solution for a p-Laplacian semipositone problem. (13th November 2005)

• Record Type: Journal Article
• Authors: Chhetri, Maya; Shivaji, R.
• Is Part Of: Boundary value problems. Volume 3(2005)
• Page Start: 323
• Page End: 327
• Publication Date: 2005-11-13
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/BVP.2005.323
• Languages: English
• ISSNs: 1687-2762

Abstract

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.