Korean Journal of Mathematics

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

  • Received : 2011.10.11
  • Accepted : 2011.11.10
  • Published : 2011.12.30
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Abstract

We give necessary and sufficient conditions such that the homogeneous differential equations of the type: $$(r(t)x^{\prime}(t))^{\prime}+q(t)x^{\prime}(t)+p(t)x(t)=0$$ are nonoscillatory where $r(t)$ > 0 for $t{\in}I=[{\alpha},{\infty})$, ${\alpha}$ > 0. Under the suitable conditions we show that the above equation is nonoscillatory if and only if for ${\gamma}$ > 0, $$(r(t)x^{\prime}(t))^{\prime}+q(t)x^{\prime}(t)+p(t)x(t-{\gamma})=0$$ is nonoscillatory. We obtain several comparison theorems.

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References

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