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Positive Solutions of the Semipositone Neumann Boundary Value Problem

    Johnny Henderson Affiliation
    ; Nickolai Kosmatov Affiliation

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
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Sep 28, 2015
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