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Delay perturbed evolution problems involving time dependent subdifferential operators

Soumia Saïdi, Mustapha Fateh Yarou (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We investigate in the present paper, the existence and uniqueness of solutions for functional differential inclusions involving a subdifferential operator in the infinite dimensional setting. The perturbation which contains the delay is single-valued, separately measurable, and separately Lipschitz. We prove, without any compactness condition, that the problem has one and only one solution.

Persistence and extinction of a stochastic delay predator-prey model under regime switching

Zhen Hai Liu, Qun Liu (2014)

Applications of Mathematics

The paper is concerned with a stochastic delay predator-prey model under regime switching. Sufficient conditions for extinction and non-persistence in the mean of the system are established. The threshold between persistence and extinction is also obtained for each population. Some numerical simulations are introduced to support our main results.

Preservation of exponential stability for equations with several delays

Leonid Berezansky, Elena Braverman (2011)

Mathematica Bohemica

We consider preservation of exponential stability for the scalar nonoscillatory linear equation with several delays x ˙ ( t ) + k = 1 m a k ( t ) x ( h k ( t ) ) = 0 , a k ( t ) 0 under the addition of new terms and a delay perturbation. We assume that the original equation has a positive fundamental function; our method is based on Bohl-Perron type theorems. Explicit stability conditions are obtained.

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