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.

Oscillation Theorems for Perturbed Second Order Nonlinear Differential Equations with Damping

Some oscillation criteria for solutions of a general perturbed second order ordinary differential equation with damping (r(t)x′ (t))′ + h(t)f (x)x′ (t) + ψ(t, x) = H(t, x(t), x′ (t)) with alternating coefficients are given. The results obtained improve and extend some existing results in the literature.

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.

Nonlinear Time-Fractional Differential Equations in Combustion Science

MSC 2010: 34A08 (main), 34G20, 80A25

Oscillation Criteria for Nonlinear Differential Equations of Second Order with Damping Term

2000 Mathematics Subject Classification: 34C10, 34C15.

Oscillation of Nonlinear Neutral Delay Differential Equations

2000 Mathematics Subject Classification: 34K15, 34C10.

Interval Oscillation for Second Order Nonlinear Differential Equations with a Damping Term

2000 Mathematics Subject Classification: 34C10, 34C15.

A Computer Algebra Application to Determination of Lie Symmetries of Partial Differential Equations

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Practical Stability and Vector-Lyapunov Functions for Impulsive Differential Equations with "Supremum"

Stability of nonlinear impulsive differential equations with "supremum" is studied. A special type of stability, combining two different measures and a dot product on a cone, is defined. Perturbing cone-valued piecewise continuous Lyapunov functions have been applied. Method of Razumikhin as well as comparison method for scalar impulsive ordinary differential equations have been employed.

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.

Integral Inequalities and Applications to Partial Differential Equations with “Maxima”

Кремена В. Стефанова - В тази статия са разрешени някои нелинейни интегрални неравенства, които включват максимума на неизвестната функция на две променливи. Разгледаните неравенства представляват обобщения на класическото неравенство на Гронуол-Белман. Значението на тези интегрални неравенства се определя от широките им приложения в качествените изследвания на частните диференциални уравнения с “максимуми” и е илюстрирано чрез някои директни приложения.

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.

Solving Differential Equations by Parallel Laplace Method with Assured Accuracy

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Differential Equations in Abstract Cones

We extend the method of quasilinearization to differential equations in abstract normal cones. Under some assumptions, corresponding monotone iterations converge to the unique solution of our problem and this convergence is superlinear or semi–superlinear

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.