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  Published Paper Details:

  Paper Title

AN OSCILLATORY CRITERIA FOR LINEAR SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS WITH DELAY

  Authors

  Sharadha panaganti,  Dr. V. Dharmaiah

  Keywords

Second order linear delay differential equations, Oscillation Criteria, Riccati technique

  Abstract


We study the Oscillatory Criteria for second order ordinary differential equation with delay of the form x?(t) + q(t) x (?(t)) = 0, on the half line R = [0,?). where ? is a constant delay, it is also a continuous functions, and q : R -> R is an integrable function. So that ?(t) <= t for every t >= 0 and lim+(t->?)??(t) ?= +?. The linear second-order ordinary differential equation of oscillatory theory is a well-established and widely studied branch of the general theory of the differential equations. The well-known Leighton- Nehari and Wintner type oscillatory solutions for ordinary differential equations also hold for delay differential equation (1). The differential equations with argumental deviations and related systems, may derive a similar set of oscillation conditions. The well-known Riccati approach for ordinary differential equations is used in this paper to provide oscillation criteria. We can infer from the equality (1) applied for the formula h(t) = x?(t)/x(t) for sufficiently large t, the non-oscillatory solution x is accurate. h?(t) = - (q(t) (x(?(t)))/(x(t)) +h^2 (t)) for large t. And applying the Riccati technique to differential equations with argument deviations requires to find suitable lower and upper bounds for the quantity (x(?(t)))/(x(t)), which is in the case of ordinary differential equations is equal to 1.

  IJCRT's Publication Details

  Unique Identification Number - IJCRT2311425

  Paper ID - 246619

  Page Number(s) - d646-d652

  Pubished in - Volume 11 | Issue 11 | November 2023

  DOI (Digital Object Identifier) -    http://doi.one/10.1729/Journal.36907

  Publisher Name - IJCRT | www.ijcrt.org | ISSN : 2320-2882

  E-ISSN Number - 2320-2882

  Cite this article

  Sharadha panaganti,  Dr. V. Dharmaiah,   "AN OSCILLATORY CRITERIA FOR LINEAR SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS WITH DELAY", International Journal of Creative Research Thoughts (IJCRT), ISSN:2320-2882, Volume.11, Issue 11, pp.d646-d652, November 2023, Available at :http://www.ijcrt.org/papers/IJCRT2311425.pdf

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ISSN: 2320-2882
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ISSN and 7.97 Impact Factor Details


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ISSN: 2320-2882
Impact Factor: 7.97 and ISSN APPROVED
Journal Starting Year (ESTD) : 2013
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