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arXiv · 1205.1844

Positive Solutions of Nonlinear Three-Point Integral Boundary-Value Problems for Second-Order Differential Equations

Faouzi Haddouchi·Slimane Benaicha
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Abstract

We investigate the existence of positive solutions to the nonlinear second-order three-point integral boundary value problem \label{eq-1} {u^{\prime \prime}}(t)+a(t)f(u(t))=0,\ 0<t<T, u(0)=βu(η),\ u(T)=α\int_{0}^ηu(s)ds, where $0<η<T$, $0<α< \frac{2T}{η^{2}}$, $0\leqβ<\frac{2T-αη^{2}}{αη^{2}-2η+2T}$ are given constants. We show the existence of at least one positive solution if $f$ is either superlinear or sublinear by applying Krasnoselskii's fixed point theorem in cones.

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Faouzi Haddouchi, Slimane Benaicha. 2013-07-04. Positive Solutions of Nonlinear Three-Point Integral Boundary-Value Problems for Second-Order Differential Equations. https://arxiv.org/abs/1205.1844

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