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Some oscillatory properties of second order non linear differential equations

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Summary

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.

References

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

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    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.

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

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

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

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

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Keywords

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