An explicit coefficient criterion for the existence of positive solutionsto the linear advanced equation

Josef Diblík; Klara Janglajew; Mária Kúdelčíková

doi:10.3934/dcdsb.2014.19.2461

Article Contents

2014, Volume 19, Issue 8: 2461-2467. Doi: 10.3934/dcdsb.2014.19.2461

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An explicit coefficient criterion for the existence of positive solutions to the linear advanced equation

1.
Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering and Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Brno
2.
Department of Difference Equations and Discrete Systems, Institute of Mathematics, University of Białystok, Białystok
3.
Department of Mathematics, University of Žilina, Žilina

Received: March 2014

Revised: April 2014

Published: October 2014

Abstract / Introduction Related Papers Cited by

Abstract

The paper is devoted to the investigation of a linear differential equation with advanced argument $\dot y(t)=c(t)y(t+\tau),$ where $\tau>0$, and the function $c\colon [t_0,\infty)\to (0,\infty)$, $t_0\in \mathbb{R}$ is bounded and locally Lipschitz continuous. New explicit coefficient criterion for the existence of a positive solution in terms of $c$ and $\tau$ is derived.

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Mathematics Subject Classification: 34K15, 34K25.

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References

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