Positive solutions of nonlinear equations via comparison with linear operators

Jeffrey R. L. Webb

doi:10.3934/dcds.2013.33.5507

Article Contents

2013, Volume 33, Issue 11&12: 5507-5519. Doi: 10.3934/dcds.2013.33.5507

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Positive solutions of nonlinear equations via comparison with linear operators

Jeffrey R. L. Webb^1,

1.
School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QW

Received: May 31, 2011

Revised: February 29, 2012

Published: October 2013

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Abstract

We discuss positive solutions of problems that arise from nonlinear boundary value problems in the particular situation where the nonlinear term $f(t,u)$ depends explicitly on $t$ and this dependence is crucial. We give new fixed point index results using comparisons with linear operators. These prove new results on existence of positive solutions under some conditions which can be sharp.

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Mathematics Subject Classification: Primary: 34B18; Secondary: 34B10, 47H07, 47H11.

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