On bounded solutions in a given set of systems of differential equations

On Bounded Solutions of Systems of Linear Functional Differential Equations

Sufficient conditions of the existence and uniqueness of bounded on real axis solutions of systems of linear functional differential equations are established. 1. Formulations of the Main Results Let R be the set of real numbers, Cloc(R, R) be the space of continuous functions u : R → R with the topology of uniform convergence on every compact interval and Lloc(R,R) be the space of locally summ...

Bounded Solutions: Differential Vs Difference Equations

We compare some recent results on bounded solutions (over Z) of nonlinear difference equations and systems to corresponding ones for nonlinear differential equations. Bounded input-bounded output problems, lower and upper solutions, Landesman-Lazer conditions and guiding functions techniques are considered.

Exact and numerical solutions of linear and non-linear systems of fractional partial differential equations

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

Existence of bounded solutions of a class of neutral systems of functional differential equations

System of functional differential equations Iterated deviations Lipschitz derivative a b s t r a c t Some results on the existence of bounded solutions together with their first derivatives of a class of neutral systems of functional differential equations with complicated deviations, which extend and unify numerous results in the literature, are proved.

Numerical Solutions of Special Class of Systems of Non-Linear Volterra Integro-Differential Equations by a Simple High Accuracy Method