Instability for solution for a class of the third order nonlinear differential equation (Q1910320)

In a joint paper with \textit{Z. Liao} [ibid. 9, No. 10, 969-984 (1988; Zbl 0751.34031)] the author obtained sufficient conditions for instability of the zero solution of a linear third-order equation with time-varying coefficients. Here he considers nonlinear third-order equations of the type \(\dddot x + a(t) \ddot x + b(t) \dot x + c(t)x = f(t,x, \dot x, \ddot x)\) with \(|f(t,x, \dot x, \ddot x) |\leq A (|x |+ |\dot x |+ |\ddot x |)\), \(A\) sufficiently small, and, using appropriate Lyapunov functions, again obtains sufficient conditions for instability of the zero solution.