Positive Solutions of the Semipositone Neumann Boundary Value Problem
Abstract
In this paper we consider the Neumann boundary value problem at resonance
−u''(t) = f t, u(t) , 0 < t < 1, u' (0) = u' (1) = 0.
We assume that the nonlinear term satisfies the inequality f(t, z) + α2z + β(t) ≥ 0, t ∈ [0, 1], z ≥ 0, where β : [0, 1] → R+, and α ≠ 0. The problem is transformed into a non-resonant positone problem and positive solutions are obtained by means of a Guo–Krasnoselskii fixed point theorem.
Keyword : Neumann boundary condition, resonanc, semipositon
How to Cite
Henderson, J., & Kosmatov, N. (2015). Positive Solutions of the Semipositone Neumann Boundary Value Problem. Mathematical Modelling and Analysis, 20(5), 578-584. https://doi.org/10.3846/13926292.2015.1087435