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Study of Stability in Nonlinear Neutral Differential Equations with Variable Delay Using Krasnoselskii–Burton’s Fixed Point

Mouataz Billah MESMOULI, Abdelouaheb Ardjouni, Ahcene Djoudi (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper, we use a modification of Krasnoselskii’s fixed point theorem introduced by Burton (see [Burton, T. A.: Liapunov functionals, fixed points and stability by Krasnoseskii’s theorem. Nonlinear Stud., 9 (2002), 181–190.] Theorem 3) to obtain stability results of the zero solution of the totally nonlinear neutral differential equation with variable delay x ' t = - a t h x t + d d t Q t , x t - τ t + G t , x t , x t - τ t . The stability of the zero solution of this eqution provided that h 0 = Q t , 0 = G t , 0 , 0 = 0 . The Caratheodory condition is used for the functions Q and G .

Sturm-Liouville systems are Riesz-spectral systems

Cédric Delattre, Denis Dochain, Joseph Winkin (2003)

International Journal of Applied Mathematics and Computer Science

The class of Sturm-Liouville systems is defined. It appears to be a subclass of Riesz-spectral systems, since it is shown that the negative of a Sturm-Liouville operator is a Riesz-spectral operator on L^2(a,b) and the infinitesimal generator of a C_0-semigroup of bounded linear operators.

Subdifferential inclusions and quasi-static hemivariational inequalities for frictional viscoelastic contact problems

Stanisław Migórski (2012)

Open Mathematics

We survey recent results on the mathematical modeling of nonconvex and nonsmooth contact problems arising in mechanics and engineering. The approach to such problems is based on the notions of an operator subdifferential inclusion and a hemivariational inequality, and focuses on three aspects. First we report on results on the existence and uniqueness of solutions to subdifferential inclusions. Then we discuss two classes of quasi-static hemivariational ineqaulities, and finally, we present ideas...

Subgroups of odd depth—a necessary condition

Sebastian Burciu (2013)

Czechoslovak Mathematical Journal

This paper gives necessary and sufficient conditions for subgroups with trivial core to be of odd depth. We show that a subgroup with trivial core is an odd depth subgroup if and only if certain induced modules from it are faithful. Algebraically this gives a combinatorial condition that has to be satisfied by the subgroups with trivial core in order to be subgroups of a given odd depth. The condition can be expressed as a certain matrix with { 0 , 1 } -entries to have maximal rank. The entries of the matrix...

Subharmonic solutions of a nonconvex noncoercive hamiltonian system

Najeh Kallel, Mohsen Timoumi (2004)

RAIRO - Operations Research - Recherche Opérationnelle

In this paper we study the existence of subharmonic solutions of the hamiltonian system J x ˙ + u * G ( t , u ( x ) ) = e ( t ) where u is a linear map, G is a C 1 -function and e is a continuous function.

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