BibTex RIS Cite

OSCILLATION THEOREMS FOR SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS

Year 2016, Volume: 29 Issue: 4, 929 - 935, 19.12.2016

Abstract

In this paper, we are concerned with the oscillations in forced second order nonlinear differential equations with nonlinear damping terms. By using clasical variational principle and averaging technique, new oscillation criteria are established, which improve and extend some recent results. Examples are also given to illustrate the results.

References

  • M.S. Keener, Solutions of a certain linear
  • nonhomogeneous second order differential
  • equations, Appl. Anal. 1 (1971) 57–63.
  • A.Skidmore, W. Leighton, On the
  • equation y '' p  x y  f  x J. Math. Anal.
  • Appl. 43 (1973) 46–55.
  • A. Skidmore, J. J. Bowers, Oscillation behavior of
  • y '' p  x y  f  x , J. Math. Anal. Appl. 49
  • (1975) 317–323.
  • S.M. Rainkin, Oscillation theorems for second
  • order nonhomogeneous linear differential
  • equations, J. Math. Anal. Appl. 53 (1976) 550–553.
  • J.S.W. Wong, Second order nonlinear forced
  • oscillations, SIAM J. Math. Anal. 19 (1988) 667–
  • F. Jiang, F. Meng, New oscillation criteria for a
  • class of second-order nonlinear forced differential
  • equations, J. Math. Anal. Appl. 336 (2007) 1476–
  • S.P. Rogovchenko, Y.V. Rogovchenko, Oscillation
  • theorems for differential equation with a nonlinear
  • damping term, J. Math. Anal. Appl. 279 (2003)
  • –134.
  • A. Tiryaki, A. Zafer, Interval oscillation of a
  • general class of second-order nonlinear differential
  • equations with nonlinear damping, Nonlinear Anal.
  • (2005) 49–63.
  • A. Tiryaki, A. Zafer, Oscillation of Second-Order
  • Nonlinear Different ial Equations with Nonlinear
  • Damping, Mathematical and Computer modelling
  • (2004) 197-208.
  • X. Zhao, F. Meng, Oscillation of second-order
  • nonlinear ODE with damping, Appl. Math.Comput.
  • (2006) 1861–1871.
  • Y. Huang, F. Meng, Oscillation of second-order
  • nonlinear ODE with damping, Appl. Math.
  • Comput. 199 (2008) 644–652.
  • A. Zhao, Y. Wang, J. Yan, Oscillation criteria for
  • second-order nonlinear differential equations with
  • nonlinear damping, Computers and Mathematics
  • with Applications 56 (2008) 542–555.
  • F. Meng, Y. Huang, Interval oscillation criteria for
  • a forced second-order nonlinear differential
  • equations with damping, Appl. Math.Comput. 218
  • (2011) 1857–1861.
  • W. Shi, Interval oscillation criteria for a forced
  • second-order differential equation with nonlinear
  • damping, Mathematical and Computer modelling
  • (2006) 170–177.
  • G.H. Hardy, J.E. Littlewood, G. Polya, Inequalities,
  • second ed., Cambridge University Press,
  • Cambridge, 1988.
Year 2016, Volume: 29 Issue: 4, 929 - 935, 19.12.2016

Abstract

References

  • M.S. Keener, Solutions of a certain linear
  • nonhomogeneous second order differential
  • equations, Appl. Anal. 1 (1971) 57–63.
  • A.Skidmore, W. Leighton, On the
  • equation y '' p  x y  f  x J. Math. Anal.
  • Appl. 43 (1973) 46–55.
  • A. Skidmore, J. J. Bowers, Oscillation behavior of
  • y '' p  x y  f  x , J. Math. Anal. Appl. 49
  • (1975) 317–323.
  • S.M. Rainkin, Oscillation theorems for second
  • order nonhomogeneous linear differential
  • equations, J. Math. Anal. Appl. 53 (1976) 550–553.
  • J.S.W. Wong, Second order nonlinear forced
  • oscillations, SIAM J. Math. Anal. 19 (1988) 667–
  • F. Jiang, F. Meng, New oscillation criteria for a
  • class of second-order nonlinear forced differential
  • equations, J. Math. Anal. Appl. 336 (2007) 1476–
  • S.P. Rogovchenko, Y.V. Rogovchenko, Oscillation
  • theorems for differential equation with a nonlinear
  • damping term, J. Math. Anal. Appl. 279 (2003)
  • –134.
  • A. Tiryaki, A. Zafer, Interval oscillation of a
  • general class of second-order nonlinear differential
  • equations with nonlinear damping, Nonlinear Anal.
  • (2005) 49–63.
  • A. Tiryaki, A. Zafer, Oscillation of Second-Order
  • Nonlinear Different ial Equations with Nonlinear
  • Damping, Mathematical and Computer modelling
  • (2004) 197-208.
  • X. Zhao, F. Meng, Oscillation of second-order
  • nonlinear ODE with damping, Appl. Math.Comput.
  • (2006) 1861–1871.
  • Y. Huang, F. Meng, Oscillation of second-order
  • nonlinear ODE with damping, Appl. Math.
  • Comput. 199 (2008) 644–652.
  • A. Zhao, Y. Wang, J. Yan, Oscillation criteria for
  • second-order nonlinear differential equations with
  • nonlinear damping, Computers and Mathematics
  • with Applications 56 (2008) 542–555.
  • F. Meng, Y. Huang, Interval oscillation criteria for
  • a forced second-order nonlinear differential
  • equations with damping, Appl. Math.Comput. 218
  • (2011) 1857–1861.
  • W. Shi, Interval oscillation criteria for a forced
  • second-order differential equation with nonlinear
  • damping, Mathematical and Computer modelling
  • (2006) 170–177.
  • G.H. Hardy, J.E. Littlewood, G. Polya, Inequalities,
  • second ed., Cambridge University Press,
  • Cambridge, 1988.
There are 50 citations in total.

Details

Journal Section Mathematics
Authors

Adil Mısır

Süleyman Öğrekçi

Publication Date December 19, 2016
Published in Issue Year 2016 Volume: 29 Issue: 4

Cite

APA Mısır, A., & Öğrekçi, S. (2016). OSCILLATION THEOREMS FOR SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS. Gazi University Journal of Science, 29(4), 929-935.
AMA Mısır A, Öğrekçi S. OSCILLATION THEOREMS FOR SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS. Gazi University Journal of Science. December 2016;29(4):929-935.
Chicago Mısır, Adil, and Süleyman Öğrekçi. “OSCILLATION THEOREMS FOR SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS”. Gazi University Journal of Science 29, no. 4 (December 2016): 929-35.
EndNote Mısır A, Öğrekçi S (December 1, 2016) OSCILLATION THEOREMS FOR SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS. Gazi University Journal of Science 29 4 929–935.
IEEE A. Mısır and S. Öğrekçi, “OSCILLATION THEOREMS FOR SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS”, Gazi University Journal of Science, vol. 29, no. 4, pp. 929–935, 2016.
ISNAD Mısır, Adil - Öğrekçi, Süleyman. “OSCILLATION THEOREMS FOR SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS”. Gazi University Journal of Science 29/4 (December 2016), 929-935.
JAMA Mısır A, Öğrekçi S. OSCILLATION THEOREMS FOR SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS. Gazi University Journal of Science. 2016;29:929–935.
MLA Mısır, Adil and Süleyman Öğrekçi. “OSCILLATION THEOREMS FOR SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS”. Gazi University Journal of Science, vol. 29, no. 4, 2016, pp. 929-35.
Vancouver Mısır A, Öğrekçi S. OSCILLATION THEOREMS FOR SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS. Gazi University Journal of Science. 2016;29(4):929-35.