scholarly journals Global stability for a class of functional differential equations with distributed delay and non-monotone bistable nonlinearity

2020 ◽  
Vol 17 (6) ◽  
pp. 7332-7352
Author(s):  
Toshikazu Kuniya ◽  
◽  
Tarik Mohammed Touaoula ◽  
Keyword(s):  
Differential Equations ◽  
Global Stability ◽  
Functional Differential Equations ◽  
Distributed Delay ◽  
Bistable Nonlinearity ◽  
Functional Differential

scholarly journals Oscillation of Fourth-Order Functional Differential Equations with Distributed Delay

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 61 ◽  
Author(s):  
Clemente Cesarano ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
All Solutions ◽  
Functional Differential ◽  
Delay Differential ◽  
Comparison Technique

In this paper, the authors obtain some new sufficient conditions for the oscillation of all solutions of the fourth order delay differential equations. Some new oscillatory criteria are obtained by using the generalized Riccati transformations and comparison technique with first order delay differential equation. Our results extend and improve many well-known results for oscillation of solutions to a class of fourth-order delay differential equations. The effectiveness of the obtained criteria is illustrated via examples.

scholarly journals Hölder Continuous Regularity of Stochastic Convolutions with Distributed Delay

2021 ◽  
Author(s):  
Kai Liu
Keyword(s):  
Differential Equations ◽  
Hilbert Spaces ◽  
Functional Differential Equations ◽  
Distributed Delay ◽  
Fundamental Solutions ◽  
Regularity Property ◽  
Hölder Continuous ◽  
Stochastic Convolutions ◽  
Retarded Functional Differential Equations ◽  
Functional Differential

AbstractIn this work, we consider the Hölder continuous regularity of stochastic convolutions for a class of linear stochastic retarded functional differential equations with distributed delay in Hilbert spaces. By focusing on distributed delays, we first establish some more delicate estimates for fundamental solutions than those given in Liu (Discrete Contin. Dyn. Syst. Ser. B 25(4), 1279–1298, 2020). Then we apply these estimates to stochastic convolutions incurred by distributed delay to study their regularity property. Last, we present some easily-verified results by considering the regularity of a class of systems whose delay operators have the same order derivatives as those in instantaneous ones.

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