Some oscillatory properties of second order non linear differential equations

  • 24 Accesses

  • 5 Citations


The aim of this note is to show that, under certain conditions, the comparìson theorems between a nonlinear second order differential equation of certain type and a linear second order differential equation hold. From this we shall be able to guarentee the oscillatory or nonoscillatory character of certain or all solutions of the considered nonlinear differential equation.


  1. [1]

    R. Reissig-G. Sansone-R. Conti,Qualitative Theorie ifferentialgleichungen, Edizioni Cremonese, Roma (1963).

  2. [2]

    E. Gagliardo,Sul comportamento degli integrali dell'equazione differenziale non lineare x″+f(x)x′+g(x)=0 con g(x) crescente e f(x) positiva per |x|>M>0. Boll. Un. Mat. Ital. (3) 8 (1953), pp. 309–314.

  3. [3]

    W. R. Utz,Properties of solutions of certain second order non linear differential equations, Proc. Amer. Math. Soc. 8 (1957), pp. 1024–1028.

  4. [4]

    Z. Opial,Sur une équation différentielle non linéaire du second ordre, Ann. Polon. Math. 8 (1960), pp. 65–69.

Download references

Author information

Additional information

Work done at the Instituto Matematico « Ulisse Dini » in Firenze.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Švec, M. Some oscillatory properties of second order non linear differential equations. Annali di Matematica 77, 179–191 (1967) doi:10.1007/BF02416942

Download citation


  • Differential Equation
  • Nonlinear Differential Equation
  • Linear Differential Equation
  • Order Differential Equation
  • Oscillatory Property