On the Asymptotic Stability of Solutions of Nonlinear Delay Differential Equations

On the Asymptotic Stability of the Solutions of Functional Differential Equations with Infinite Delay

On Global Asymptotic Stability of Solutions of Differential Equations(1)

I ■V *■ • • • iV*TC | V j j J j (1.1) x'=/(x) in which f(x) is of class C1 on En. Let J(x) = (df/dx) denote the Jacobian matrix of /and let H(x) = (J+J*)/2 be the symmetric part of J(x). One of the results of [2] is to the effect that if (1.2) /(0) = 0 and (1.3) H(x) is negative definite (for fixed x ^ 0), then x = 0 is a globally asymptotically stable solution of (1.1); i.e., every solution x ...

Asymptotic stability and asymptotic solutions of second-order differential equations

We improve, simplify, and extend on quasi-linear case some results on asymptotical stability of ordinary second-order differential equations with complex-valued coefficients obtained in our previous paper [G.R. Hovhannisyan, Asymptotic stability for second-order differential equations with complex coefficients, Electron. J. Differential Equations 2004 (85) (2004) 1–20]. To prove asymptotic stab...

On the stability of solutions of nonlinear differential equations of fifth order with delay

Criteria for global asymptotic stability of a null solution of a nonlinear differential equation of fifth order with delay x(t) + ψ(x(t− r), x′(t− r), x′′(t− r), x′′′(t− r), x(t− r))x(t) +f(x′′(t− r), x′′′(t− r)) + α3x(t) + α4x(t) + α5x(t) = 0 are obtained by using Lyapunov’s second method. By defining a Lyapunov functional, sufficient conditions are established, which guarantee the null soluti...

Topological soliton solutions of the some nonlinear partial differential equations

In this paper, we obtained the 1-soliton solutions of the symmetric regularized long wave (SRLW) equation and the (3+1)-dimensional shallow water wave equations. Solitary wave ansatz method is used to carry out the integration of the equations and obtain topological soliton solutions The physical parameters in the soliton solutions are obtained as functions of the dependent coefficients. Note t...