Electron. J. Diff. Equ.,
Vol. 2014 (2014), No. 93, pp. 114.
Existence and multiplicity of positive periodic
solutions for secondorder functional differential
equations with infinite delay
Qiang Li, Yongxiang Li
Abstract:
In this article, the existence and multiplicity results of positive
periodic solutions are obtained for the secondorder functional
differential equation with infinite delay
where
are continuous
periodic
functions,
is defined by
for
,
denotes the Banach space of bounded continuous function
with the norm
,
and
is a nonnegative continuous functional.
The existence conditions concern with the first eigenvalue of the associated
linear periodic boundary problem. Our discussion is based on the fixed point
index theory in cones.
Submitted September 22, 2013. Published April 4, 2014.
Math Subject Classifications: 34C25, 47H10.
Key Words: Secondorder functional differential equations; first eigenvalue;
positive periodic solution; cone; fixed point index.
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Qiang Li
Department of Mathematics
Northwest Normal University
Lanzhou 730070, China
email: lznwnuliqiang@126.com


Yongxiang Li
Department of Mathematics
Northwest Normal University
Lanzhou 730070, China
email: liyxnwnu@163.com, Phone 8609317971111

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