BibTex RIS Kaynak Göster

OSCILLATION THEOREMS FOR SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS

Yıl 2016, Cilt: 29 Sayı: 4, 929 - 935, 19.12.2016

Öz

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.

Kaynakça

  • 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.
Yıl 2016, Cilt: 29 Sayı: 4, 929 - 935, 19.12.2016

Öz

Kaynakça

  • 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.
Toplam 50 adet kaynakça vardır.

Ayrıntılar

Bölüm Mathematics
Yazarlar

Adil Mısır

Süleyman Öğrekçi

Yayımlanma Tarihi 19 Aralık 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 29 Sayı: 4

Kaynak Göster

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. Aralık 2016;29(4):929-935.
Chicago Mısır, Adil, ve Süleyman Öğrekçi. “OSCILLATION THEOREMS FOR SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS”. Gazi University Journal of Science 29, sy. 4 (Aralık 2016): 929-35.
EndNote Mısır A, Öğrekçi S (01 Aralık 2016) OSCILLATION THEOREMS FOR SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS. Gazi University Journal of Science 29 4 929–935.
IEEE A. Mısır ve S. Öğrekçi, “OSCILLATION THEOREMS FOR SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS”, Gazi University Journal of Science, c. 29, sy. 4, ss. 929–935, 2016.
ISNAD Mısır, Adil - Öğrekçi, Süleyman. “OSCILLATION THEOREMS FOR SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS”. Gazi University Journal of Science 29/4 (Aralık 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 ve Süleyman Öğrekçi. “OSCILLATION THEOREMS FOR SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS”. Gazi University Journal of Science, c. 29, sy. 4, 2016, ss. 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.