Annali di Matematica Pura ed Applicata

, Volume 109, Issue 1, pp 23–38 | Cite as

On the existence of oscillatory solutions to nonlinear differential equations

  • Lynn H. Erbe
  • James S. Muldowney


A general change of variable technique is combined with appropriate energy functions to show the existence of oscillatory solutions to nonlinear ordinary second order differential equations.


Differential Equation Energy Function Nonlinear Differential Equation Variable Technique General Change 
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  1. [1]
    F. V. Atkinson,On second-order non-linear oscillations, Pacific J. Math.,5 (1955) pp. 643–647.zbMATHMathSciNetGoogle Scholar
  2. [2]
    S. Belohorec,Oscillatory solutions of certain nonlinear differential equations of the second order, (Czech.) Mat.-Fyz. Casopis Sloven. Akad. Vied.,11 (1961), 4, pp. 250–255.zbMATHGoogle Scholar
  3. [3]
    S. Belohorec, On some properties of the equation y″(x)+f(x)yα(x)=0,0<α<1, Mat. Casopis. Sloven. Akad. Vied,17 (1967), 1, pp. 10–19.zbMATHMathSciNetGoogle Scholar
  4. [4]
    S. Belohorec,A criterion for oscillation and nonoscillation, Acta F.R.N. Univ. Comen. Mathematica,20 (1969), pp. 75–79.MathSciNetGoogle Scholar
  5. [5]
    K. L. Chiou,A nonoscillation theorem for the superlinear case of second order differential equations y″+yF(y2,x)=0, Notices Amer. Math. Soc.,19 (November, 1972), A-797.Google Scholar
  6. [6]
    C. V. Coffman -J. S. V. Wong,On a second order nonlinear oscillation problem, Trans. Amer. Math. Soc.,147 (1970), pp. 357–366.CrossRefMathSciNetGoogle Scholar
  7. [7]
    C. V. Coffman -J. S. W. Wong,Oscillation and nonoscillation of solutions of generalized Emden-Fowler equations, Trans. Amer. Math. Soc.,167 (1972), pp. 399–434.CrossRefMathSciNetGoogle Scholar
  8. [8]
    J. W. Heidel -Don B. Hinton,The existence of oscillatory solutions for a nonlinear differential equation, SIAM J. Math. Anal.,3 (1972), pp. 344–351.CrossRefMathSciNetGoogle Scholar
  9. [9]
    J. W. Heidel -I. T. Kiguradze,Oscillatory solutions for a generalized sublinear differential equation, Notices Amer. Math. Soc., A19 (1972), p. 793.Google Scholar
  10. [10]
    D. V. Izyumova,On the conditions for the oscillation and nonoscillation of solutions of nonlinear second order differential equations, (Russian), Differential'nye Uravneniya,2 (1966), pp. 1572–1586; (translated in Differential Equations,2 (1966), pp. 814–821).zbMATHGoogle Scholar
  11. [11]
    M. Jasny,On the existence of an oscillating solution of the nonlinear differential equation of the second order y″+f(x)y 2n−1=0,f(x)>0, (Russian), Casopis Pest. Mat.,85 (1960) pp. 78–83.zbMATHMathSciNetGoogle Scholar
  12. [12]
    J. Kurzweil,A note on oscillatory solutions of the equation y″+f(x)y 2n−1=0, (Russian), Casopis Pest. Mat.,85 (1960), pp. 357–358.zbMATHMathSciNetGoogle Scholar
  13. [13]
    R. A. Moore -Z. Nehari,Nonoscillation theorems for a class of nonlinear differential equations, Trans. Amer. Math. Soc.,93 (1959), pp. 30–52.CrossRefMathSciNetGoogle Scholar
  14. [14]
    J. S. Muldowney,Discontinuous scalar functions and ordinary differential equations, (to appear).Google Scholar
  15. [15]
    Z. Nehari,On a class of nonlinear second order differential equations, Trans. Amer. Math. Soc.,95 (1960), pp. 101–123.CrossRefzbMATHMathSciNetGoogle Scholar
  16. [16]
    Z. Nehari,A nonlinear oscillation problem, J. Differential Equations,5 (1969), pp. 452–460.CrossRefzbMATHMathSciNetGoogle Scholar
  17. [17]
    G. Sansone,Su un'equazione differenziale non lineare della fisica nucleare, Istituto Nazionale di Alta Matematica, Symposia Mathematica,6 (1971), pp. 3–139.zbMATHMathSciNetGoogle Scholar
  18. [18]
    J. S. W. Wong,On second order nonlinear oscillation, Funkcial. Ekvac.,11 (1969,) pp. 207–234.zbMATHGoogle Scholar

Copyright information

© Fondazione Annali di Matematica Para ed Applicata 1975

Authors and Affiliations

  • Lynn H. Erbe
    • 1
  • James S. Muldowney
    • 1
  1. 1.EdmontonCanada

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