Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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OSCILLATION CRITERIA OF DIFFERENTIAL EQUATIONS OF SECOND ORDER

  • Received : 2011.08.03
  • Accepted : 2011.09.10
  • Published : 2011.09.30
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Abstract

We give sufficient conditions that the homogeneous differential equations : for $t{\geq}t_0$(> 0), $$x^{{\prime}{\prime}}(t)+q(t)x^{\prime}(t)+p(t)x(t)=0,\\x^{{\prime}{\prime}}(t)+q(t)x^{\prime}(t)+F(t,x({\phi}(t)))=0$$, are oscillatory where $0{\leq}{\phi}(t)$, 0 < ${\phi}^{\prime}(t)$, $\lim_{t\to{\infty}}{\phi}(t)={\infty}$. and $F(t,u){\cdot}sgn$ $u{\leq}p(t)|u|$. We obtain comparison theorems.

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References

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