Exact null controllability of semilinear integrodifferential systems in Hilbert spaces

Sufficient conditions for exact null controllability of the semilinear integrodifferential systems in Hilbert spaces are obtained. It is shown that under some natural conditions exact null controllability of the semilinear integrodifferential system is implied by the exact null controllability of the corresponding linear system with additive term. An application to partial integrodifferential equations is given.     

Regularity of solutions of evolution integrodifferential equations with deviating argument

In this paper we prove the existence of mild and classical solutions of delay integrodifferential equation and delay integrodifferential evolution equations with nonlocal condition in Banach spaces. The regularity solutions of integrodifferential evolution equations interconnected with viscoelastic material is derived to guarantee the stabilization. The results are established by using the resolvent operators and the fixed point principles. Finally, an example is given to show the potential of the proposed techniques.     

An Identification Problem for an Ultraparabolic Integrodifferential Equation

We prove the well posedness of an inverse problem related to an abstract integrodifferential problem in two time variables with applications to ultraparabolic partial integrodifferential equations of Volterra type.     

On some new integrodifferential inequalities of the Wendroff type

This paper presents some new integrodifferential inequalities in two independent variables of the Wendroff type which can be used in the analysis of a class of hyperbolic partial integrodifferential equations as handy tools.     

Construction of periodic solutions of integrodifferential equations of viscoelasticity

A theorem on the estimation of the periodic solutions of a linear integrodifferential equation and a theorem of existence and uniqueness of the periodic solution of a nonlinear integrodifferential equation are presented without proof.     

The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces

In this paper we prove the existence of solutions of certain kinds of nonlinear fractional integrodifferential equations in Banach spaces. Further, Cauchy problems with nonlocal initial conditions are discussed for the aforementioned fractional integrodifferential equations. At the end, an example is presented.     

Controllability of nonlinear neutral evolution integrodifferential systems

Sufficient conditions for controllability of nonlinear neutral evolution integrodifferential systems in a Banach space are established. The results are obtained by using the resolvent operators and the Schaefer fixed-point theorem. An application to partial integrodifferential equation is given.     

On a solution to fractional order integrodifferential equations with analytic semigroups

In this paper we study a class of fractional order integrodifferential equations considered in an arbitrary Banach space. Using the theory of analytic semigroups we establish the existence, uniqueness and regularity of a mild solution to these fractional order integrodifferential equations.     

Variation of parameters formulae with initial time difference for linear integrodifferential equations

This article investigates the relationship between an unperturbed integrodifferential system and a perturbed integrodifferential system that have different initial positions and an initial time difference (ITD). Variation of parameter techniques are employed to obtain integral formulae and to define Lyapunov-like functions.