Stability criteria for certain third order nonlinear delay differential equations
Summary: We study the asymptotic stability of the trivial solution of third order nonlinear delay differential equation \[ x'''(t) + f(x(t), x^\prime (t))x^{\prime \prime }(t) + g(x(t - r), x^\prime (t - r)) + h(x(t - r)) = 0, \] where \(r > 0\) is a constant delay. In proving our result we make use of Lyapunov's second method by constructing a Lyapunov functional.
nonlinear delay differential equation of third order
scientific article; zbMATH DE number 5535150
scientific article