Asymptotic behavior of solutions of second-order nonlinear impulsive differential equations. (English) Zbl 1135.34302

The authors investigate impulsive second-order differential equations of the kind \[ \begin{gathered} (r(t) x'(t))'+ p(t) x'(t)+ Q(t, x(t))= 0,\quad t= t_k,\\ x'(t^+_k)= M_k(x'(t_k)),\;x(t^+_k)= N_k(x(t_k)),\;t= t_k,\;k= 1,2,\dots, t\geq t_0.\end{gathered}\tag{1} \] They derive sufficiently conditions for \(\liminf_{t\to\infty}|x(t)|= 0\), where \(x(t)\) is solution of (1).


34A37 Ordinary differential equations with impulses
34D05 Asymptotic properties of solutions to ordinary differential equations
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