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Oscillation of second order linear differential equations with impulses. (English) Zbl 1130.34314

We use the associated Riccati techniques and the equivalence transformation to discuss the oscillation and the nonoscillation of the second order linear ordinary differential equation with impulses of the form
\[ \begin{cases} (a(t)x'(t))'+p(t)x(t)=0, & t\geq t_0,\;t\neq t_k,\\ x(t^+_k)=b_kx(t_k),\quad x'(t^+_k)=c_kx'(t_k), & k=1,2,\dots.\end{cases} \]
Some examples are also given which show that the oscillation of impulsive differential equations can be caused by impulsive perturbations, though the corresponding classical equation admits a nonoscillatory solution.

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34A37 Ordinary differential equations with impulses
34A30 Linear ordinary differential equations and systems
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References:

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