Existence of solutions of functional-differential inclusion in nonconvex case
Existence of solutions to a paratingent equation with delayed argument.
Existence results for impulsive evolution differential equations with state-dependent delay.
Existence results for impulsive partial neutral functional differential inclusions.
Existence results for second-order impulsive functional differential inclusions.
Existence theorem for functional-differential contingent equations
Existence theory for functional initial value problems of ordinary differential equations.
Extremal Solutions for a Class of Functional Differential Equations
We study, in Carathéodory assumptions, existence, continuation and continuous dependence of extremal solutions for an abstract and rather general class of hereditary differential equations. By some examples we prove that, unlike the nonfunctional case, solved Cauchy problems for hereditary differential equations may not have local extremal solutions.
First order integro-differential equations in Banach algebras involving Carathéodory and discontinuous nonlinearities.
Frequency analysis of preconditioned waveform relaxation iterations
The error analysis of preconditioned waveform relaxation iterations for differential systems is presented. This analysis extends and refines previous results by Burrage, Jackiewicz, Nørsett and Renaut by incorporating all terms in the expansion of the error of waveform relaxation iterations in the Laplace transform domain. Lower bounds for the size of the window of rapid convergence are also obtained. The theory is illustrated for waveform relaxation methods applied to differential systems resulting...
Functional differential equations
The method of quasilinearization is a well-known technique for obtaining approximate solutions of nonlinear differential equations. In this paper we apply this technique to functional differential problems. It is shown that linear iterations converge to the unique solution and this convergence is superlinear.
Functional differential equations - a reciprocity principle.
Functional differential equations in Banach spaces: Growth and decay of solutions.
Functional-differential equations with Riemann-Liouville integrals in the nonlinearities
A sufficient condition for the nonexistence of blowing-up solutions to evolution functional-differential equations in Banach spaces with the Riemann-Liouville integrals in their right-hand sides is proved. The linear part of such type of equations is an infinitesimal generator of a strongly continuous semigroup of linear bounded operators. The proof of the main result is based on a desingularization method applied by the author in his papers on integral inequalities with weakly singular kernels....
Fuzzy solutions for neutral functional differential equations with nonlocal conditions.
Generalized functional-differential equations of neutral type
Generalized solutions of functional differential inclusions.
Gleichmäßig asymptotische Stabilität stationäre Punkte bei Differential-Differenzengleichungen.
Global dynamics of a delay differential system of a two-patch SIS-model with transport-related infections
We describe the global dynamics of a disease transmission model between two regions which are connected via bidirectional or unidirectional transportation, where infection occurs during the travel as well as within the regions. We define the regional reproduction numbers and the basic reproduction number by constructing a next generation matrix. If the two regions are connected via bidirectional transportation, the basic reproduction number characterizes the existence of equilibria as well as...
Global error estimation in the numerical solution of retarded differential equations by Euler's method
In this paper Zadunaisky's technique is used to estimate the global error propagated in the numerical solution of the system of retarded differential equations by Euler's method. Some numerical examples are given.