## 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).

### MSC:

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

### References:

 [1] Bainov, D.; Simeonov, P., Oscillation theorem of impulsive differential equations, (1998), International Publications · Zbl 0960.34515 [2] Lakshmikantham, V.; Bainov, D.D.; Simeonov, P., Theory of impulsive differential equations, (1989), World Scientific Singapor · Zbl 0719.34002 [3] Wu, Xiu-li; Chen, Si-Yang; Ji, Hong, Oscillation of a class of second-order nonlinear ODE with impulses, Appl. math. comput., 138, 181-188, (2003) · Zbl 1034.34038 [4] Rogorchenko, Y.V., Oscillation theorem for second order differential equations with damping, Nonlinear anal., 41, 1005-10288, (2000) [5] Yang, Qigui, Interval oscillation criterion for forced second order nonlinear ODE with oscillatory potential, Appl. math. comput., 13, 49-64, (2003) · Zbl 1030.34034 [6] Peng, M.S.; Ge, W.G., Oscillation criteria for second order nonlinear differential equations with impulses, Comput. math. appl., 39, 217-225, (2000) · Zbl 0948.34044 [7] Wang, Qi-ru, Oscillation and asymptotics for second order half linear differential equation, Appl. math. comput., 112, 253-266, (2001) · Zbl 1030.34031
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.