Boundary-Value Problems for almost Nonlinear Singularly Perturbed Systems of Ordinary Differential Equations

A boundary-value problems for almost nonlinear singularly perturbed systems of ordinary differential equations are considered. An asymptotic solution is constructed under some assumption and using boundary functions and generalized inverse matrix and projectors.

Integral Manifolds and Bounded Solutions of Singularly Perturbed Systems of Impulsive Differential Equations

Sufficient conditions for the existence of bounded solutions of singularly perturbed impulsive differential equations are obtained. For this purpose integral manifolds are used.

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.

Existence and Uniqueness of Solutions for Partial Differential-Functional Equations of the First Order with Deviating Argument of the Derivative of Unknown Function

We consider the existence and uniqueness problem for partial differential-functional equations of the first order with the initial condition for which the right-hand side depends on the derivative of unknown function with deviating argument.

Application of Lyapunov's Direct Method to the Existence of Integral Manifolds of Impulsive Differential Equations

The present paper investigates the existence of integral manifolds for impulsive differential equations with variable perturbations. By means of piecewise continuous functions which are generalizations of the classical Lyapunov’s functions, sufficient conditions for the existence of integral manifolds of such equations are found.

Integral Manifolds and Perturbations of the Nonlinear Part of Systems of Autonomous Differential Equations with Impulses at Fixed Moments

* This investigation was supported by the Bulgarian Ministry of Science and Education under Grant MM-7.

Solutions of Analytical Systems of Partial Differential Equations

In this paper are examined some classes of linear and non-linear analytical systems of partial differential equations. Compatibility conditions are found and if they are satisfied, the solutions are given as functional series in a neighborhood of a given point (x = 0).

Mean-Periodic Solutions of Retarded Functional Differential Equations

In this paper we present a spectral criterion for existence of mean-periodic solutions of retarded functional differential equations with a time-independent main part.

Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology

Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37

Comparative Analysis of Viscoelastic Models Involving Fractional Derivatives of Different Orders

Mathematics Subject Classification: 74D05, 26A33

On a Class of Fractional Type Integral Equations in Variable Exponent Spaces

2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30

Stability in Terms of Two Measures for Differential Equations with “Maxima”

Атанаска Георгиева, Стела Глухчева, Снежана Христова - Изследвана е устойчивостта на нелинейни диференциални уравнения с “максимуми” по отношение на две мерки. Приложени са две различни мерки за началните условия и за решението. Използван е методът на Разумихин, а също така и методът на сравнението на обикновени скаларни диференциални уравнения. Приложението на получените резултати и достатъчни условия за устойчивост е илюстрирано с пример.

Asymptotic Expansion of Solution for Almost Regular and Weakly Perturbed Systems of Ordinary Differential Equations

Л. И. Каранджулов, Н. Д. Сиракова - В работата се прилага методът на Поанкаре за решаване на почти регулярни нелинейни гранични задачи при общи гранични условия. Предполага се, че диференциалната система съдържа сингулярна функция по отношение на малкия параметър. При определени условия се доказва асимптотичност на решението на поставената задача.

Oscillation Properties of Some Functional Fourth Order Ordinary Differential Equations

2010 Mathematics Subject Classification: 34A30, 34A40, 34C10.

Hypoellipticity of Anisotropic Partial Differential Equations

2002 Mathematics Subject Classification: 35S05