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Zbl 1063.34004
Luo, Jiaowan
Second-order quasilinear oscillation with impulses.
(English)
[J] Comput. Math. Appl. 46, No. 2-3, 279-291 (2003). ISSN 0898-1221

The author considers the second-order impulsive differential equation $$\biggl( r(t)\bigl\vert x'(t)\bigr\vert^{\alpha-1} x'(t)\biggr)'+ f \bigl(t, x(t)\bigr)=0, \quad t\ge t_0,\ t\ne t_k,\ k=1,2,3,\dots$$ $$x(t_k^+)= g_k \bigl(x(t_k)\bigr),\ x'(t^+_k)=h_k\bigl(x'(t_k)\bigr),\ k=1,2,3, \dots$$ $$x(t^+_0)=x_0,\ x'(t^+_0)= x'(t_0),$$ $$0\le t_0<t_1 <\cdots<t_k< \dots,\ \lim t_k=\infty\ (k\to\infty).$$ Sufficiently conditions for every solution to be oscillatory are derived.
MSC 2000:
*34A37 Differential equations with impulses
34C10 Qualitative theory of oscillations of ODE: Zeros, etc.

Keywords: Oscillation; Second-order quasilinear equation; Impulse

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