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首页> 外文期刊>Journal of applied mathematics >Interval oscillation criteria for super-half-linear impulsive differential equations with delay
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Interval oscillation criteria for super-half-linear impulsive differential equations with delay

机译:具时滞的超半线性脉冲微分方程的区间振动准则

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We study the following second-order super-half-linear impulsive differential equations with delay [ r (t) γ (x' (t)) ] ' + p (t) γ (x (t - σ)) + q (t) f (x (t - σ)) = e (t), t ≠ τ k, x (t +) = a k x (t), x' (t +) = b k x' (t), t = τ _k, where t ≥ t _0 ∈ R, φ _(z.ast;)(u) = | u | ~(*-1) u, σ is a nonnegative constant, { τ _k} denotes the impulsive moments sequence with τ 1 <τ 2 σ. By some classical inequalities, Riccati transformation, and two classes of functions, we give several interval oscillation criteria which generalize and improve some known results. Moreover, we also give two examples to illustrate the effectiveness and nonemptiness of our results.
机译:我们研究以下具有延迟[r(t)γ(x'(t))]'+ p(t)γ(x(t-σ))+ q(t的二阶超半线性脉冲微分方程)f(x(t-σ))= e(t),t≠τk,x(t +)= akx(t),x'(t +)= bkx'(t),t =τ_k,其中t≥t _0∈R,φ_(z.ast;)(u)= |你〜(*-1)u,σ为非负常数,{τ_k}表示τ1 <τ2 <? <τk <α,lim _(k→∞)τ_k =∞,τ_(k + 1)-τ_k>σ。通过一些经典的不等式,Riccati变换和两类函数,我们给出了几种区间振动准则,这些准则可以推广和改进一些已知的结果。此外,我们还举两个例子来说明我们的结果的有效性和非无效性。

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