An application of an avery type fixed pointtheorem to a second order antiperiodicboundary value problem

Jeffrey W.  Lyons

doi:10.3934/proc.2015.0775

Article Contents

2015, Volume 2015: 775-782. Doi: 10.3934/proc.2015.0775 open access

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An application of an avery type fixed point theorem to a second order antiperiodic boundary value problem

Jeffrey W. Lyons^1,

1.
Department of Mathematics, Nova Southeastern University, 3301 College Avenue, Fort Lauderdale, FL 33314

Received: August 31, 2014

Revised: January 31, 2015

Published: October 2015

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Abstract

In this article, we show the existence of an antisymmetric solution to the second order boundary value problem $x''+f(x(t))=0,\; t\in(0,n)$ satisfying antiperiodic boundary conditions $x(0)+x(n)=0,\; x'(0)+x'(n)=0$ using an Avery et. al. fixed point theorem which itself is an extension of the traditional Leggett-Williams fixed point theorem. The antisymmetric solution satisfies $x(t)=-x(n-t)$ for $t\in[0,n]$ and is nonnegative, nonincreasing, and concave for $t\in[0,n/2]$. To conclude, we present an example.

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Mathematics Subject Classification: Primary: 34B15.

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