Weakly bounded 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...

Application of Tau Approach for Solving Integro-Differential Equations with a Weakly Singular Kernel

In this work, the convection-diffusion integro-differential equation with a weakly singular kernel is discussed. The  Legendre spectral tau method is introduced for finding the unknown function. The proposed method is based on expanding the approximate solution as the elements of a shifted Legendre polynomials. We reduce the problem to a set of algebraic equations by using operational matrices....

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.

Partial Differential Equations on Bounded Domains

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.