Page 1

Displaying 1 – 2 of 2

Showing per page

On discreteness of spectrum of a functional differential operator

Sergey Labovskiy, Mário Frengue Getimane (2014)

Mathematica Bohemica

We study conditions of discreteness of spectrum of the functional-differential operator u = - u ' ' + p ( x ) u ( x ) + - ( u ( x ) - u ( s ) ) d s r ( x , s ) on ( - , ) . In the absence of the integral term this operator is a one-dimensional Schrödinger operator. In this paper we consider a symmetric operator with real spectrum. Conditions of discreteness are obtained in terms of the first eigenvalue of a truncated operator. We also obtain one simple condition for discreteness of spectrum.

On functional differential inclusions in Hilbert spaces

Myelkebir Aitalioubrahim (2012)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We prove the existence of monotone solutions, of the functional differential inclusion ẋ(t) ∈ f(t,T(t)x) +F(T(t)x) in a Hilbert space, where f is a Carathéodory single-valued mapping and F is an upper semicontinuous set-valued mapping with compact values contained in the Clarke subdifferential c V ( x ) of a uniformly regular function V.

Currently displaying 1 – 2 of 2

Page 1