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Oscillatory and Non Oscillatory Behavior of the Equation Y''' + P0tβY' + q0tδY = 0 by Using Integral Conditions of Oscillation


Affiliations
1 Dept. of Mathematics, Synergy Institute of Engineering and Technology Dhenkanal, Odisha, India
2 Dept of Mathematics, S. B. Women’s College, Cuttack, Odisha, India
3 Dept of Mathematics, Ravenshaw University, Cuttack, Odisha, India
     

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In this paper we derive different oscillation and non oscil- lation criteria for the equation y''' + p0tβy' + q0tδy = 0 using integral conditions of oscillation of third order linear differential equation.

Keywords

Oscillation, Non Oscillation, Third Order Differential Equations, Integral Condition for Oscillation, Euler Cauchy Equation.
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  • J. H. Barrett, Oscillation Theory of Ordinary linear Differential Equation, Advances in Math., 3 (1969), 415 – 509.
  • T. A. Chanturiya and I. T. Kiguradze, Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations, Nauka, Moscow, 1990.
  • J. Dzurina, Asymptotic properties of third order differential equations with deviating argument, Czech. Math. J., 44 (1994),163 –172.
  • L. Erbe. Existence of oscillatory solutions and asymptotic behavior for a class of third order linear diferential equations, Pacific J. Math., 64 (1976), 369 –385.
  • M. Gregus, Linear Differential Equation of the Third Order, Veda, Bratislava., 1981.
  • M. Hanan, Oscillation criteria for a third order linear differential equations, Pacific J. Math., 11 (1961), 919 –944.
  • J. W. Heidel, Qualitative behavior of solutions of a third order nonlinear differential equation, Pacific J. Math., 27 (1968), 507 –526.
  • N. N. Khvedelidze and T. A .Chanturiya, Oscillation of solutions of third order linear ordinary differential equations, Differencialnye Uravneniya., 27 no.3,4 (1991), 452 –460, 611–618.
  • I. T. Kiguradze, On the oscillation of solutions of the equation dm/ dtm +a(t)|u|nsignu = 0, Mat. Sb., 65 (1964), 172 –187.
  • I. T. Kiguradze, Some Singular Value Problems For Ordinary Differential Equations, University Press, Tbilisi., 1975.
  • A. C. Lazer, The behavior of solutions of the differential equation y'''+p(x)y' +q(x)y = 0, Pacific J. Math., 17 (1966), 435 –466.
  • A. Skerlik, An Integral condition of oscillation for equation y''' +p(t)y' +q(t)y = 0 with nonnegative coefficients, Archivum Mathematicum(Brno)., 31 (1995), 155 –161.
  • A. Skerlik, Oscillation theorems for third order nonlinear differential equations, Math. Slovaca., 42 (1992), 471 –484.
  • C. A. Swanson, Comparison and Oscillation Theory of Linear Differential Equations, Academic Press, New York, London, 1968.
  • A. Skerlik, Integral criteria of oscillation for a third order linear differential equation, Math. Slovaca, 45 (1995), 403 –412.

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  • Oscillatory and Non Oscillatory Behavior of the Equation Y''' + P0tβY' + q0tδY = 0 by Using Integral Conditions of Oscillation

Abstract Views: 228  |  PDF Views: 0

Authors

J. K. Pati
Dept. of Mathematics, Synergy Institute of Engineering and Technology Dhenkanal, Odisha, India
D. K. Dalai
Dept of Mathematics, S. B. Women’s College, Cuttack, Odisha, India
R. B. Dash
Dept of Mathematics, Ravenshaw University, Cuttack, Odisha, India

Abstract


In this paper we derive different oscillation and non oscil- lation criteria for the equation y''' + p0tβy' + q0tδy = 0 using integral conditions of oscillation of third order linear differential equation.

Keywords


Oscillation, Non Oscillation, Third Order Differential Equations, Integral Condition for Oscillation, Euler Cauchy Equation.

References