Oscillatory Periodic Solutions for Two Differential-Difference Equations Arising in Applications

Rong Cheng

Abstract and Applied Analysis, 2011, vol. 2011, 1-12

Abstract:

We study the existence of oscillatory periodic solutions for two nonautonomous differential-difference equations which arise in a variety of applications with the following forms: x ̇ ( t ) = - f ( t , x ( t - r ) ) and x ̇ ( t ) = - f ( t , x ( t - s ) ) - f ( t , x ( t - 2 s ) ) , where f ∈ C ( R × R , R ) is odd with respect to x, and r , s > 0 are two given constants. By using a symplectic transformation constructed by Cheng (2010) and a result in Hamiltonian systems, the existence of oscillatory periodic solutions of the above-mentioned equations is established.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:635926

DOI: 10.1155/2011/635926

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