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Uniform Stability In Nonlinear Infinite Delay Volterra Integro-differential Equations Using Lyapunov Functionals

Youssef Raffoul; Habib Rai — 2016

Nonautonomous Dynamical Systems

In [10] the first author used Lyapunov functionals and studied the exponential stability of the zero solution of finite delay Volterra Integro-differential equation. In this paper, we use modified version of the Lyapunov functional that were used in [10] to obtain criterion for the stability of the zero solution of the infinite delay nonlinear Volterra integro-differential equation [...]

Necessary and sufficient conditions for stability of Volterra integro-dynamic equation on time scales

Youssef N. Raffoul — 2016

Archivum Mathematicum

In this research we establish necessary and sufficient conditions for the stability of the zero solution of scalar Volterra integro-dynamic equation on general time scales. Our approach is based on the construction of suitable Lyapunov functionals. We will compare our findings with known results and provides application to quantum calculus.

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Currently displaying 1 – 16 of 16

Uniform Stability In Nonlinear Infinite Delay Volterra Integro-differential Equations Using Lyapunov Functionals

Necessary and sufficient conditions for stability of Volterra integro-dynamic equation on time scales

Inequalities that lead to exponential stability and instability in delay difference equations.

Periodic solutions for neutral nonlinear differential equations with functional delay.

Exponential analysis of solutions of functional differential equations with unbounded terms.

Positive periodic solutions of nonlinear functional difference equations.

Positive solutions of three-point nonlinear second order boundary value problem.

Boundedness and exponential stability of highly nonlinear stochastic differential equations.

Positive periodic solutions of functional discrete systems and population models.

Exponential stability of dynamic equations on time scales.

Periodicity and stability in neutral nonlinear dynamic equations with functional delay on a time scale.

Boundedness in functional dynamic equations on time scales.

Eigenvalue problems for a three-point boundary-value problem on a time scale.

Periodicity and stability in neutral nonlinear differential equations with functional delay.

Existence, uniqueness and constructive results for delay differential equations.

Impulsive dynamic equations on a time scale.