Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Oscillation Criteria for Certain Nonlinear Differential Equations with Damping

  • Zheng, Zhaowen (Department of Mathematical Science, Qufu Normal University) ;
  • Zhu, Siming (Department of Mathematical and computational science, Sun Yat-Sen University)
  • Received : 2004.10.28
  • Published : 2006.06.23
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Abstract

Using the integral average method, we establish some oscillation criteria for the nonlinear differential equation with damped term $$a(t)|{x}^{\prime}(t)|^{\sigma-1}{x}^{\prime}(t)^{\prime}+p(t)|{x}^{\prime}(t)|^{\sigma-1}{x}^{\prime}(t)+q(t)f(x(t))=0,\;{\sigma}>1$$, where the functions $a,\;p$ and $q$ are real-valued continuous functions defined on $[t_o,{\infty})$ with $a(t)>0,\;f(x){\in}C^1(\mathbb{R})$ and $\frac{f^{\prime}(u)}{|f^{({\sigma}-1)/{\sigma}}(u)|}{\geq}k>0$ for $u{\neq}0$.

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References

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