OSCILLATORY PROPERTY OF SOLUTIONS FOR A CLASS OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH PERTURBATION

  • Zhang, Quanxin (Department of Mathematics and Information Science, Binzhou University) ;
  • Qiu, Fang (Department of Mathematics and Information Science, Binzhou University) ;
  • Gao, Li (Department of Mathematics and Information Science, Binzhou University)
  • Received : 2009.10.03
  • Accepted : 2009.11.17
  • Published : 2010.05.30

Abstract

This paper is concerned with oscillation property of solutions of a class of second order nonlinear differential equations with perturbation. Four new theorems of oscillation property are established. These results develop and generalize the known results. Among these theorems, two theorems in the front develop the results by Yan J(Proc Amer Math Soc, 1986, 98: 276-282), and the last two theorems in this paper are completely new for the second order linear differential equations.

Keywords

References

  1. Ladde G.S., Lakshmikantham V. and Zhang B.G.: Oscillation theory of differential equations with deviating arguments. Marcel Dekker, New York(1987).
  2. Yan J.R.: Oscillation Theory of ordinary differential equations. Shanxi education press, Taiyuan (1992). (in Chinese)
  3. Wintner A.: A criterion of oscillatory stability, Quart: Appl. Math., 7,115-117(1949).
  4. Yan J.R.: Oscillation theorems for second order linear differential equations with damping, Proc. Amer. Math. Soc., 98, 276-282(1986). https://doi.org/10.1090/S0002-9939-1986-0854033-4
  5. Cakmak D.: Oscillation criteria for nonlinear second order differential equations with damping, Ukrainian Mathematical Journal, 60(5), 799-809(2008). https://doi.org/10.1007/s11253-008-0088-6
  6. Rogovchenko Yu.V.: On oscillation of a second order nonlinear delay differential equation, Funkcial. Ekvac., 3, 1-29(2000).
  7. Ohriska J.: Oscillation of second order linear delay differential equations, Cent. Eur. J. Math., 6(3), 439-452(2008). https://doi.org/10.2478/s11533-008-0030-z
  8. Zhang Q.X., Yan J.R.: Oscillatory behavior of a second order nonlinear differential equation with damping, Journal of Systems Science and Mathematical Science, 24(3), 296-302(2004). (in Chinese)
  9. Yan J.R., Zhang Q.X.: Oscillatory theorems for second order nonlinear differential equations with damping, Journal of Systems Science and Mathematical Science, 13(3), 276-278(1993). (in Chinese)
  10. Cecchi M., Marini M.: Oscillatory and nonoscillatory behavior of a second order functional differential equation, Rocky Mount. J. Math., 22, 1259-1276(1992). https://doi.org/10.1216/rmjm/1181072653
  11. Philos C.G., Purnaras I.K.: On the oscillation of second order nonlinear differential equations, Arch. Math., 59, 260-271(1992). https://doi.org/10.1007/BF01197323
  12. Zhang Q.X., Wang L.: Oscillatory behavior of solutions for a class of second order nonlinear differential equation with perturbation, Acta Appl. Math., doi: 10.1007/s10440-0099483-8 (2009).