Izvorni znanstveni članak
On the stability of solutions of nonlinear differential equations of fifth order with delay
Cemil Tunç
orcid.org/0000-0003-2909-8753
; Department of Mathematics, Faculty of Arts and Sciences, Yüzüncü Yil University,Van,Turkey
Sažetak
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 (x(t-r),x^{\prime }(t-r),x^{\prime \prime
}(t-r),x^{\prime
\prime \prime }(t-r),x^{(4)}(t-r))x^{(4)}(t) \\
&&\quad+f(x^{\prime \prime }(t-r),x^{\prime \prime \prime }(t-r))+\alpha
_{3}x^{\prime \prime }(t)+\alpha _{4}x^{\prime }(t)+\alpha _{5}x(t)=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.
Ključne riječi
stability; Lyapunov functional; differential equation; fifth order; delay
Hrčak ID:
53235
URI
Datum izdavanja:
10.6.2010.
Posjeta: 1.319 *