On the stability of solutions of nonlinear differential equations of fifth order with delayReport as inadecuate




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Mathematical Communications, Vol.15 No.1 June 2010. -

Criteria for global asymptotic stability of a null solution

of a nonlinear differential equation of fifth order with delay%

\begin{eqnarray*}

&&x^{5}t+\psi xt-r,x^{\prime }t-r,x^{\prime \prime

}t-r,x^{\prime

\prime \prime }t-r,x^{4}t-rx^{4}t \\

&&\quad+fx^{\prime \prime }t-r,x^{\prime \prime \prime }t-r+\alpha

{3}x^{\prime \prime }t+\alpha {4}x^{\prime }t+\alpha {5}xt=0

\end{eqnarray*}

are obtained by using Lyapunov-s second method. By defining a

Lyapunov functional, sufficient conditions are established, which

guarantee the null solution of this equation is globally

asymptotically stable. Our result consists of a new theorem on the

subject.

stability; Lyapunov functional; differential equation; fifth order; delay



Author: Cemil Tunç - orcid.org-0000-0003-2909-8753 ; Department of Mathematics, Faculty of Arts and Sciences, Yüzüncü Yil University,

Source: http://hrcak.srce.hr/



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