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On the oscillation of certain functional differential equations

Ravi P. Agarwal|S. R. Grace|S. Dontha
대한수학회 (The Korean Mathematical Society)|2004.04|대한수학회논문집 (Communications of the KMS)|제19권 제2호|pp. 307-319

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Abstract

In this paper, we establish some new oscillation criteria for thefunctional differential equations of the formbegin{array}{l}displaystyle frac{d}{dt}left(frac{1}{a_{n-1}(t)}frac{d}{dt}left(frac{1}{a_{n-2}(t)}frac{d}{dt}left(cdots left( frac{1}{a_1(t)}frac{d}{dt}x(t)right) cdotsright) right) right)^{alpha} displaystyle + delta left[f_1left(t,x[g_1(t)],frac{d}{dt}x[h_1(t)]right)+f_2left(t,x[g_2(t)], frac{d}{dt}x[h_2(t)]right)right]{hskip-0.13cm}={hskip-0.06cm}0 ddend{array}via comparing it with some other functionaldifferential equations whose oscillatory behavior is known.

참고문헌 (11)

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  5. "On the Oscillation of Higher Order Differential Equations with Deviating Arguments", 38, pp.185~199 (1999)
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  8. "Oscillation Criteria for Retarded Differential Equations with a Nonlinear Damping Term", 51, pp.68~82 (1996)
  9. "} Oscillatory Theory of Delay Differential Equations withApplications" (1991), Oxford Univ. Press
  10. "} Oscillation of Functional Differential Equations with GeneralDeviating Arguments", pp.445~ (1985)
  11. "} Some Comparison Criteria in Oscillation Theory", pp.176~ (1984)

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