## Abstract In this paper we apply quarkonial decomposition to the ordinary differential equation of delay type __f__ β²(__x__) = __f__ (__x__ β 1), __x__ β₯ 1. We shall derive an explicit formula in terms of the quarkonial decomposition. (Β© 2008 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
A Massera Type Criterion for Linear Functional Differential Equations with Advance and Delay
β Scribed by Li Yong; Lin Zhenghua; Li Zhaoxing
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 116 KB
- Volume
- 200
- Category
- Article
- ISSN
- 0022-247X
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β¦ Synopsis
In this note, a Massera type criterion for the existence of periodic solutions for linear functional differential equations with advance and delay is established. Because of the presence of an advanced argument, the definition of the fundamental solution operator seems unknown. Hence a method different from the usual one is employed. Applications to periodic problems for nonlinear equations are also given.
π SIMILAR VOLUMES
## Abstract Sufficient conditions are established for oscillation of second order super half linear equations containing both delay and advanced arguments of the form equation image where __Ο~Ξ΄~__ (__u__) = |__u__ |^__Ξ΄__ β1^__u__; __Ξ±__ > 0, __Ξ²__ β₯ __Ξ±__, and __Ξ³__ β₯ __Ξ±__ are real numbers; __k
## Abstract In this paper we obtain instability and stability criteria for second order linear impulsive differential equations with periodic coefficients. Further, a Lyapunov type inequality is also established. (Β© 2008 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
This paper deals with the existence of periodic solutions for some partial functional differential equations with infinite delay. We suppose that the linear part is nondensely defined and satisfies the HilleαYosida condition. In the nonlinear case we give several criteria to ensure the existence of