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

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

On a Stochastic Partial Differential Equation with a Noisy Term

2000 Mathematics Subject Classification: 60H15, 60H40

A Simple Example of Localized Parametric Resonance for the Wave Equation

2000 Mathematics Subject Classification: 35L05, 35P25, 47A40.

Oscillation of Nonlinear Neutral Delay Differential Equations

2000 Mathematics Subject Classification: 34K15, 34C10.

Solutions of Fractional Diffusion-Wave Equations in Terms of H-functions

MSC 2010: 35R11, 42A38, 26A33, 33E12

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

Oscillation Theorems for Second Order Sublinear Ordinary Differential Equations

Oscillation criteria are given for the second order sublinear non-autonomous differential equation. (r(t) (x)x′(t))′ + q(t)g(x(t)) = (t). These criteria extends and improves earlier oscillation criteria of Kamenev, Kura, Philos and Wong. Oscillation criteria are also given for second order sublinear damped non-autonomous differential equations.

A Fractional Analog of the Duhamel Principle

Mathematics Subject Classification: 35CXX, 26A33, 35S10

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

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

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.

Explicit Solutions of Nonlocal Boundary Value Problems, Containing Bitsadze-Samarskii Constraints

MSC 2010: 44A35, 35L20, 35J05, 35J25

Nonlinear Time-Fractional Differential Equations in Combustion Science

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

Stability and Instability of Solitary Wave Solutions of a Nonlinear Dispersive System of Benjamin-Bona-Mahony Type

2000 Mathematics Subject Classification: 35B35, 35B40, 35Q35, 76B25, 76E30.

Oscillation Criteria for First Order Delay Differential Equations

2000 Mathematics Subject Classification: 34K15.

Exact Solutions of Nonlocal Boundary Value Problems for One- and Two-Dimensional Heat Equation

Иван Хр. Димовски, Юлиан Ц. Цанков - Предложен е метод за намиране на явни решения на клас двумерни уравнения на топлопроводността с нелокални условия по пространствените променливи. Методът е основан на директно тримерно операционно смятане. Класическата дюамелова конволюция е комбинирана с две некласически конволюции за операторите ∂xx и ∂yy в една тримерна конволюция. Съответното операционно смятане използва мултипликаторни частни. Мултипликаторните частни позволяват да се продължи принципът на Дюамел за пространствените променливи и да се намерят явни решения на разглежданите гранични задачи. Общите разглеждания са приложени в случая на гранични условия от типа на Йонкин. Намерени са експлицитни решения в затворен вид.