Forced Oscillation Criteria for Nonlinear Hyperbolic Equations via Riccati Method

Shoukaku, Yutaka

  • Received : 2012.11.12
  • Accepted : 2016.02.06
  • Published : 2016.03.23


In this paper, we consider the nonlinear hyperbolic equations with forcing term. Some suffcient conditions for the oscillation are derived by using integral averaging method and a generalized Riccati technique.


Forced oscillation;hyperbolic equations;Riccati inequality;interval criteria


  1. R. P. Agarwal, M. Bohner and W. T. Li, Nonoscillation and oscillation : Theory for Functional Differential Equations, Marcel Dekker, New York, 2004.
  2. S. Cui, Z. Xu, Interval oscillation theorems for second order nonlinear partial delay differential equations, Differ. Equ. Appl., 1(2009), 379-391.
  3. J. R. Graef and P. W. Spikes, On the oscillatory behavior of solutions of second order nonlinear differential equations, Czechoslovak Math. J., 36(1986), 275-284.
  4. W. T. Li and X. Li, Oscillation criteria for second-order nonlinear differential equations with integrable coeffcient, Appl. Math. Lett., 13(2000), 1-6.
  5. H. Usami, Some oscillation theorem for a class of quasilinear elliptic equations, Ann. Mat. Pura Appl., 175(1998), 277-283.
  6. Y. Shoukaku, Forced oscillations of nonlinear hyperbolic equations with functional arguments via Riccati method, Appl. Appl. Math., 1(2010), 122-153.
  7. Y. Shoukaku and N. Yoshida, Oscillations of nonlinear hyperbolic equations with functional arguments via Riccati method, Appl. Math. Comput., 217(2010), 143-151.
  8. P. J. Y. Wong and R. P. Agarwal, Oscillatory behavior of solutions of certain second order nonlinear differential equations, J. Math. Anal. Appl., 198(1996), 337-354.
  9. N. Yoshida, Oscillation Theory of Partial Differential Equations, World Scientific Publishing Co. Pte. Ltd., 2008.