Positive solution curves of an infinite semipositone problem
Date
2018-11-01
Authors
Dhanya, Rajendran
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article we consider the infinite semipositone problem -∆u = λƒ(u) in Ω, a smooth bounded domain in ℝN, and u = 0 on ∂Ω, where ƒ(t) = tq - t-β and 0 < q, β < 1. Using stability analysis we prove the existence of a connected branch of maximal solutions emanating from infinity. Under certain additional hypothesis on the extremal solution at λ = Λ we prove a version of Crandall-Rabinowitz bifurcation theorem which provides a multiplicity result for λ ∈ (Λ, Λ + ε).
Description
Keywords
Semipositone problems, Topological methods, Bifurcation theory
Citation
Dhanya, R. (2018). Positive solution curves of an infinite semipositone problem. <i>Electronic Journal of Differential Equations, 2018</i>(178), pp. 1-14.
Rights
Attribution 4.0 International