Two periodic solutions of second-order neutral functional differential equations. (English) Zbl 1118.34063
The authors investigate the existence, multiplicity and nonexistence of positive periodic solutions for the following second-order neutral functional differential equations
\[
(x(t)-cx(t-\delta))''+a(t)x(t)=\lambda b(t)f(x(t-\tau(t))),
\]
where \(\lambda\) is a positive parameter, \(c\) and \(\delta\) are constants and \(| c| \not=1\). The criteria essentially depend on the limits of the function \(f(u)/u\) as \(u\) tends to zero or infinity. The approach is based on the Krasnoselskii fixed point theorem.
Reviewer: Meng Fan (Changchun)
MSC:
| 34K13 | Periodic solutions to functional-differential equations |
| 34K40 | Neutral functional-differential equations |
| 47H10 | Fixed-point theorems |
Keywords:
Krasnoselskii fixed point theoremReferences:
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