Hyers–Ulam stability of functional equations with a square-symmetric operation

The stability of the functional equation f(x ○ y) = H(f(x), f(y)) (x, y ∈ S) is investigated, where H is a homogeneous function and ○ is a square-symmetric operation on the set S. The results presented include and generalize the classical theorem of Hyers obtained in 1941 on the stability of the Cauchy functional equation.

Instability considerations for various difference equations derived from the diffusion equation,

"Prepared for American Mathematical Society Meeting, Los Angeles, California, Nov. 27, 1954."

Algebraical problems, producing simple and quadratic equations, with their solutions : designed as an introduction to the higher branches of analytics /

Mode of access: Internet.

A treatise on differential equations, with a collection of examples arranged in classes, corresponding to the several divisions of the subject.

Mode of access: Internet.

Uniqueness for boundary value problems for second order finite difference equations

We establish maximum principles for second order difference equations and apply them to obtain uniqueness for solutions of some boundary value problems.

Continuous Dependence of Solutions of Quasidifferential Equations with Non-Fixed Time of Impulses

In this article on quasidifferential equation with non-fixed time of impulses we consider the continuous dependence of the solutions on the initial conditions as well as the mappings defined by these equations. We prove general theorems for quasidifferential equations from which follows corresponding results for differential equations, differential inclusion and equations with Hukuhara derivative.

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.

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.

Properties of Lp (K)-Solutions of Linear Nonhomogeneous Impulsive Differential Equations with Unbounded Linear Operator

Sufficient conditions for the existence of Lp(k)-solutions of linear nonhomogeneous impulsive differential equations with unbounded linear operator are found. An example of the theory of the linear nonhomogeneous partial impulsive differential equations of parabolic type is given.

Noninear Integral Inequalities Involving Maxima

Снежана Христова, Кремена Стефанова, Лозанка Тренкова - В статията се изучават някои интегрални неравенства, които съдържат макси-мума на неизвестната функция на една променлива. Разглежданите неравенства са обобщения на класическото неравенство на Бихари. Значимостта на тези интегрални неравенства се дълже на широкото им приложение при качественото изследванене на различни свойства на решенията на диференциални уравнения с “максимум” и е илюстрирано с някои директни приложения.

On the 3-Wave Equations with Constant Boundary Conditions

2010 Mathematics Subject Classification: 37K40, 35Q15, 35Q51, 37K15.

Monte Carlo Algorithm for Solving Integral Equations with Polynomial Non-Linearity. Parallel Implementation

An iterative Monte Carlo algorithm for evaluating linear functionals of the solution of integral equations with polynomial non-linearity is proposed and studied. The method uses a simulation of branching stochastic processes. It is proved that the mathematical expectation of the introduced random variable is equal to a linear functional of the solution. The algorithm uses the so-called almost optimal density function. Numerical examples are considered. Parallel implementation of the algorithm is also realized using the package ATHAPASCAN as an environment for parallel realization.The computational results demonstrate high parallel efficiency of the presented algorithm and give a good solution when almost optimal density function is used as a transition density.

Anomalous Singularities for Hyperbolic Equations with Degeneracy of Infinite Order

2002 Mathematics Subject Classification: 35L80

On the Zeros of the Solutions to Nonlinear Hyperbolic Equations with Delays

2002 Mathematics Subject Classification: Primary 35В05; Secondary 35L15

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

2000 Mathematics Subject Classification: 34C10, 34C15.