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

Rong Cheng

Abstract and Applied Analysis, 2011, vol. 2011, issue 1

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-2s)), 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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https://doi.org/10.1155/2011/635926

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:635926

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