Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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INTERVAL OSCILLATION THEOREMS FOR SECOND-ORDER DIFFERENTIAL EQUATIONS

  • Bin, Zheng (School of Mathematics and Information Science, Shandong University of Technology)
  • Published : 2009.05.31
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Abstract

In this paper, we are concerned with a class of nonlinear second-order differential equations with a nonlinear damping term and forcing term: $$(r(t)k_1(x(t),x'(t)))'+p(t)k_2(x(t),x'(t))x'(t)+q(t)f(x(t))=0$$. Passage to more general class of equations allows us to remove a restrictive condition usually imposed on the nonlinearity. And, as a consequence, our results apply to wider classes of nonlinear differential equations. Some illustrative examples are considered.

Keywords

References

  1. Svitkana P. Rogovchenko and Yuri V. Rogovchenko, Oscillation theorems for differential equations with a nonlinear damping term, J. Math. Ann. Appl. 279(2003)121-134. https://doi.org/10.1016/S0022-247X(02)00623-6
  2. J.W.Baker, Oscillation theorems for a second order damped nonlinear equation, SIAM J. Appl. Math. 25(1973)37-40. https://doi.org/10.1137/0125007
  3. L. E. Bobisud, Oscillation of solutions of damped nonlinear equations, SIAM J. Appl. Math. 19(1970)601-606. https://doi.org/10.1137/0119059
  4. B. Ayanlar. A. Tiryaki, Oscillation theorems for nonlinear second order differential equation with damping, Acta Math. Hungar. 89(2000)1-13. https://doi.org/10.1023/A:1026716923088
  5. S. P. Rogovchenko, Yu. V. Rogovchenko, Oscillation of differential equations with damping, Dynam.Contin.Discrete Impuls. Systems Ser. A Math. Anal. 10(2003)447-461.
  6. M. K. Kwong and A. Zettle. Integral inequalities and second order linear oscillation. J. Differential Equations. 45(1982)16-33. https://doi.org/10.1016/0022-0396(82)90052-3
  7. M. A. Ei-sayed. An oscillation criterion for a forced second order linear differential equations. Proc. Amer. Math. Soc. 118(1993)813-817.
  8. C. C. Huang. Oscillation and nonoscillation for second order linear differential equations. J. Math. Anal. Appl. 210(1997)712-723. https://doi.org/10.1006/jmaa.1997.5428
  9. Q. Kong. Interval criteria for oscillation of second-order linear ordinary differential equations. J. Math. Anal. Appl. 229(1999)258-270. https://doi.org/10.1006/jmaa.1998.6159
  10. Wan-Tong Li and Ravi P. Agarwal. Interval oscillation criteria ralated to integral averaging technique for certain nonlinear differential equations. J. Math. Anal. Appl. 245(2000)171-188. https://doi.org/10.1006/jmaa.2000.6749
  11. Zhaowen Zheng. Note on Wong's paper. J. Math. Anal. Appl. 274(2002)466-473. https://doi.org/10.1016/S0022-247X(02)00297-4
  12. James S. W. Wong. On Kamenev-Type oscillation theorems for second-order differential equations with damping. J. Math. Anal. Appl. 258(2001)244-257. https://doi.org/10.1006/jmaa.2000.7376
  13. Fanwei Meng and Yuangong Sun. Interval criteria for oscillation of linear Hamiltonian systems. Mathematical and Computer Modelling, 40(2004)735-743. https://doi.org/10.1016/j.mcm.2004.10.005