Rocky Mountain Journal of Mathematics

Oscillation of $n$th order superlinear dynamic equations on time scales

Lynn Erbe, Jia Baoguo, and Allan Peterson

Full-text: Open access

Article information

Source
Rocky Mountain J. Math., Volume 41, Number 2 (2011), 471-491.

Dates
First available in Project Euclid: 2 May 2011

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1304345449

Digital Object Identifier
doi:10.1216/RMJ-2011-41-2-471

Mathematical Reviews number (MathSciNet)
MR2794449

Zentralblatt MATH identifier
1216.34100

Subjects
Primary: 34K11: Oscillation theory 39A10: Difference equations, additive 39A99: None of the above, but in this section

Keywords
Oscillation superlinear dynamic equation isolated time scale

Citation

Erbe, Lynn; Baoguo, Jia; Peterson, Allan. Oscillation of $n$th order superlinear dynamic equations on time scales. Rocky Mountain J. Math. 41 (2011), no. 2, 471--491. doi:10.1216/RMJ-2011-41-2-471. https://projecteuclid.org/euclid.rmjm/1304345449


Export citation

References

  • R.P. Agarwal, Difference equations and inequalities, Marcel Dekker, New York, 2000.
  • R.P. Agarwal, S.R. Grace and D. O'Regan, Oscillation theory for difference and functional differential equations, Kluwer Academic Publishers, Dordrecht, 2000.
  • F.V. Atkinson, On second order nonlinear oscillaton, Pacific J. Math. 5 (1955), 643-647.
  • Jia Baoguo, Kiguradze-type oscillation theorems for third order superlinear dynamic equations on time scales, submitted for publication.
  • Jia Baoguo, Lynn Erbe and Allan Peterson, Kiguradze-type oscillation theorems for second order superlinear dynamic equation on time scales, Canad. Math. Bull., in press.
  • M. Bohner and A. Peterson, Dynamic equations on time scales: An introduction with applications, Birkhäuser, Boston, 2001.
  • –––, eds., Advances in dynamic equations on time scales, Birkhäuser, Boston, 2003.
  • J.W. Hooker and W.T. Patula, A second order nonlinear difference equation: Oscillation and asymptotic behavior, J. Math. Anal. Appl. 91 (1983), 9-29.
  • Victor Kac and Pokman Cheung, Quantum calculus, Universitext, Springer, New York, 2001.
  • I.T. Kiguradze, A note on the oscillation of solutions of the equation $u^\pp+a(t)u^n \text\rm sgn\, u=0$, Casopis Pest. Mat. 92 (1967), 343-350.
  • –––, On the oscillation of solutions of some ordinary differential equations, Dokl. Akad. Nauk SSSR 144 (1962), 33-36 (in Russian).
  • I. Ličko and M. Švec, Le caractere oscillatoire des solution de l'equation $y^(n)+f(x)y^\alpha=0, n>1$, Czechos.Math. J. 13 (1963), 481-491.
  • A.B. Mingarelli, Volterra-Stieltjes Integral equations and generalized differential equations, Lecture Notes in Mathematics 989 Springer-Verlag, 1983.
  • G.H. Ryder and D.V.V. Wend, Oscillation of solutions of certain ordinary differential equations of $n$-th order, Proc. Amer. Math. Soc. 25 (1970), 463-469.
  • J.S.W. Wong, Oscillation criteria for second order nonlinear differential equations involving general means, J. Math. Anal. Appl. 24 (2000), 489-505.