Bounded solutions in a given set of differential systems

Stability results for set solution of fuzzy integro-differential systems

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...

Functions of Bounded Variation as Solutions of Differential Systems

1. This paper investigates certain linear differential systems whose solutions are required to be merely functions of bounded variation. Subsequently the equivalence of such problems with appropriate integral equations with Lebesgue integrals and, also, their equivalence to certain integral equations with Stieltjes integrals is established. This study is a generalization of differential systems...

Polynomially bounded solutions of the Loewner‎ ‎differential equation in several complex variables

‎We determine the‎ ‎form of polynomially bounded solutions to the Loewner differential ‎equation that is satisfied by univalent subordination chains of the‎ ‎form $f(z,t)=e^{int_0^t A(tau){rm d}tau}z+cdots$‎, ‎where‎ ‎$A:[0,infty]rightarrow L(mathbb{C}^n,mathbb{C}^n)$ is a locally‎ ‎Lebesgue integrable mapping and satisfying the condition‎ ‎$$sup_{sgeq0}int_0^inftyleft|expleft{int_s^t‎ ‎[A(tau)...

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.