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Positive periodic solutions for a second-order functional differential equation

Yongxiang Li* and Qiang Li

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Department of Mathematics, Northwest Normal University, Lanzhou, 730070, People’s Republic of China

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Boundary Value Problems 2012, 2012:140 doi:10.1186/1687-2770-2012-140

Published: 27 November 2012

Abstract

In this paper, the existence results of positive ω-periodic solutions are obtained for the second-order functional differential equation

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/140/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/140/mathml/M1">View MathML</a>

where <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/140/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/140/mathml/M2">View MathML</a> is a continuous function which is ω-periodic in t, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/140/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/140/mathml/M3">View MathML</a> is a ω-periodic function, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/140/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/140/mathml/M4">View MathML</a>. Our discussion is based on the fixed point index theory in cones.

MSC: 34C25, 47H10.

Keywords:
functional differential equation; positive periodic solution; cone; fixed point index