Stability of solutions to nonlinear wave equations with switching time delay

Long Time Behaviour of Solutions to Nonlinear Wave Equations

G(u,u',u") = 0, (1) where u = u(x, x,..., x), and u', u" denote all the first and second partial derivatives of u. For simplicity we will assume here that both u and G are scalars and denote by ua, uab, the partial derivatives dau and respectively dahu; a,b =1,2, ..., n+1. Let u (x) be a given solution of (1). Our equation is said to be elliptic or hyperbolic at u°(x) according to whether the (...

EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR NEUTRAL DIFFERANCE EQUATIONS WITH VARIABLE DELAY

Hyers-Ulam and Hyers-Ulam-Rassias stability of nonlinear integral equations with delay

In this paper we are going to study the Hyers{Ulam{Rassias typesof stability for nonlinear, nonhomogeneous Volterra integral equations with delayon nite intervals.

Stability of solutions to abstract evolution equations with delay

An equation u̇ = A(t)u+B(t)F (t, u(t−τ)), u(t) = v(t),−τ ≤ t ≤ 0 is considered, A(t) and B(t) are linear operators in a Hilbert space H, u̇ = du dt , F : H → H is a non-linear operator, τ > 0 is a constant. Under some assumption on A(t), B(t) and F (t, u) sufficient conditions are given for the solution u(t) to exist globally, i.e, for all t ≥ 0, to be globally bounded, and to tend to zero at a s...

New explicit and Soliton Wave Solutions of Some Nonlinear Partial Differential Equations with Infinite Series Method

To start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ODE. Then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. It is required to state that the infinite series method is a well-organized method for obtaining exact s...