Linear Hyperbolic Functional-Differential Equations with Essentially Bounded Right-Hand Side

On the averaging of differential inclusions with Fuzzy right hand side with the average of the right hand side is absent

In this article we consider the averaging method for differential inclusions with fuzzy right-hand side for the case when the limit of a method of an average does not exist. 

Multivalued Semilinear Neutral Functional Differential Equations with Nonconvex-valued Right-hand Side

On the Darboux problem for linear hyperbolic functional-differential equations

Theorems on the Fredholm alternative and well-posedness of the Darboux problem ∂2u(t, x) ∂t ∂x = `(u)(t, x) + q(t, x), u(t, x0) = φ(t) for t ∈ [a, b], u(t0, x) = ψ(x) for x ∈ [c, d] are established, where ` : C(D;R) → L(D;R) is a linear bounded operator, q ∈ L(D;R), t0 ∈ [a, b], x0 ∈ [c, d], φ : [a, b]→ R, ψ : [c, d]→ R are absolutely continuous functions, and D = [a, b] × [c, d]. New sufficien...

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...

Implicit integral equations with discontinuous right-hand side

We consider the integral equation h(u(t)) = f R I g(t, x)u(x) dx , with t ∈ [0, 1], and prove an existence theorem for bounded solutions where f is not assumed to be continuous.