Existence nonexistence and multiplicity of periodic solutions for a kind of functional differential equation with parameter

In this paper, we study the existence, multiplicity and nonexistence of positive ω -periodic solutions for a kind of second-order delay functional differential equation with parameter u ̈ ( t ) + a ( t ) u ( t ) = λ f ( t , u ( t − τ 0 ( t ) ) , u ( t − τ 1 ( t ) ) , … , u ( t − τ n ( t ) ) ) by emp...

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Bibliographic Details
Published in:Nonlinear analysis 2009, Vol.70 (1), p.433-443
Main Author: Wu, Yuexiang
Format: Article
Language:English
Subjects:
Algebra
Commutative rings and algebras
Difference and functional equations, recurrence relations
Exact sciences and technology
Existence
Finite differences and functional equations
Fixed point theorem
Functional differential equation
Mathematical analysis
Mathematics
Multiplicity
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Periodic solution
Sciences and techniques of general use
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Summary:In this paper, we study the existence, multiplicity and nonexistence of positive ω -periodic solutions for a kind of second-order delay functional differential equation with parameter u ̈ ( t ) + a ( t ) u ( t ) = λ f ( t , u ( t − τ 0 ( t ) ) , u ( t − τ 1 ( t ) ) , … , u ( t − τ n ( t ) ) ) by employing the Krasnoselskii fixed point theorem for a cone map, where λ > 0 is a parameter; some new results are obtained. As an application of our results, we discuss an example.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2007.12.011