Existence of positive solutions for a class of p-Laplacian superlinear semipositone problems. Issue 5 (21st July 2015)

• Record Type: Journal Article
• Authors: Chhetri, M.; Drábek, P.; Shivaji, R.
• Is Part Of: Proceedings. Volume 145:Issue 5(2015)
• Page Start: 925
• Page End: 936
• Publication Date: 2015-07-21
• Subjects: p-Laplacian, -- systems, -- semipositone, -- superlinear, -- positive solutions; Primary 35J60, -- 35J25, -- 35J65; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0308210515000220
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract : We consider a quasilinear elliptic problem of the form where λ > 0 is a parameter, 1 < p < 2 and Ω is a strictly convex bounded domain in ℝ N, N > p, with C 2 boundary ∂Ω . The nonlinearity f : [0, ∞) → ℝ is a continuous function that is semipositone ( f (0) < 0) and p -superlinear at infinity. Using degree theory, combined with a rescaling argument and uniform L ∞ a priori bound, we establish the existence of a positive solution for λ small. Moreover, we show that there exists a connected component of positive solutions bifurcating from infinity at λ = 0. We also extend our study to systems.