Stability results for nonlinear functional differential equations using fixed point methods

2018 ◽  
Vol 29 (2) ◽  
pp. 671-686 ◽  
Author(s):  
Guiling Chen ◽  
Dingshi Li ◽  
Onno van Gaans ◽  
Sjoerd Verduyn Lunel
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Nonlinear Functional ◽  
Fixed Point Methods ◽  
Functional Differential ◽  
Stability Results

Three Positive Periodic Solutions of Nonlinear Functional Differential Equations with Impulse Effects

2011 ◽  
Vol 403-408 ◽  
pp. 1319-1321
Author(s):  
Lei Wang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Functional Differential Equations ◽  
Positive Periodic Solutions ◽  
Nonlinear Functional ◽  
Functional Differential

In this paper, a type of nonlinear functional differential equations with impulse effects are studied by using the Leggett-Williams fixed point theorem.

scholarly journals Ulam-Hyers-Rassias Stability of Stochastic Functional Differential Equations via Fixed Point Methods

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Abdellatif Ben Makhlouf ◽  
Lassaad Mchiri ◽  
Mohamed Rhaima
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Stochastic Systems ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Fixed Point Methods ◽  
Functional Differential ◽  
The Stability ◽  
Rassias Stability ◽  
Stochastic Functional

The Ulam-Hyers-Rassias stability for stochastic systems has been studied by many researchers using the Gronwall-type inequalities, but there is no research paper on the Ulam-Hyers-Rassias stability of stochastic functional differential equations via fixed point methods. The main goal of this paper is to investigate the Ulam-Hyers Stability (HUS) and Ulam-Hyers-Rassias Stability (HURS) of stochastic functional differential equations (SFDEs). Under the fixed point methods and the stochastic analysis techniques, the stability results for SFDE are investigated. We analyze two illustrative examples to show the validity of the results.

scholarly journals Some Properties of Solutions of a Functional-Differential Equation of Second Order with Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Veronica Ana Ilea ◽  
Diana Otrocol
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Operator Theory ◽  
Functional Differential Equations ◽  
Picard Operator ◽  
Functional Differential ◽  
Weakly Picard Operator ◽  
Stability Results

Existence, uniqueness, data dependence (monotony, continuity, and differentiability with respect to parameter), and Ulam-Hyers stability results for the solutions of a system of functional-differential equations with delays are proved. The techniques used are Perov’s fixed point theorem and weakly Picard operator theory.

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