Comparison results for oscillation of nonlinear differential equations

Nonlinear Differential Equations and Applications

Volumn 6, Issue 2, 1999, Pages 173-190

  Cecchi, Mariella ^a   Marini, Mauro ^a   Villari, Gabriele ^a  

^a UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Comparison results; Oscillation

Indexed keywords

EID: 0004382267     PISSN: 10219722     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000300050071     Document Type: Article

References (33)

1. F.V. ATKINSON, On second order nonlinear oscillation, Pacif. J. Math. 5, 643-647 (1955).
2. S. BELOHOREC, Oscillatory solutions of a certain nonlinear differential equation of second order, Mat.Fyz. Casopis Sloven. Akad. Vied. 11, 250-255 (1961) (in Slovac).
3. R. BLASKO, J.R. GRAEF, M. HACIK, P.W. SPIKES, Oscillatory behavior of solutions of nonlinear differential equations of the second order, J. Math. Anal. Appl. 151, 330-343 (1990).
4. G.J. BUTLER, The existence of continuable solutions of a second order differential equation, Can. J. Math. XXIX, 3, 472-479 (1977).
5. G.J.BUTLER, L.H. ERBE, A generalization of Olech-Opial-Wazewski oscillation criteria to second order nonlinear equations, Nonlinear Analysis, T.M.A. 11, 2, 207-219 (1987).
6. M. CECCHI, M. MARINI, Gab. VILLARI, Integral criteria for a classification of solutions of linear differential equations, J. Diff. Equal. 99, 381-397 (1992).
7. M. CECCHI, M. MARINI, Gab. VILLARI, Topological and variational approaches for nonlinear oscillation: an extension of a Bhatia result, Proc. First World Congress Nonlinear Analysts,Walter de Gruyter, Berlin, 1505-1514 (1996).
8. M. CECCHI, M. MARINI, Gab. VILLARI, On some classes of continuable solutions of a nonlinear differential equation, J. Diff. Equal. 118, 2, 403-419 (1995).
9. C.V. COFFMAN, J.S.W. WONG, Oscillation and nonoscillation of solutions of generalized Emden-Fowler equations, Trans. Amer. Math. Soc. 167, 399-434 (1972).
10. C.V. COFFMAN, J.S.W. WONG, Oscillation and nonoscillation theorems for second order ordinary differential equations, Funke. Ekvac. 15, 119-130 (1972).
11. A. ELBERT, T. KUSANO, Oscillation and non-oscillation theorems for a class of second order quasilinear differential equations, Acta Math. Hung. 56, 3-4, 325-336 (1990).
12. L.H. ERBE, Nonoscillation criteria for second order nonlinear differential equations, J. Math. Anal. Appl. 108, 515-527 (1985).
13. L.H. ERBE, H. LU, Nonoscillation theorems for second order nonlinear differential equations, Funkc. Ekvac. 33, 2, 227-244 (1990).
14. S.R. GRACE, Oscillation theorems for nonlinear differential equations of second order, J. Math. Anal. Appl. 171, 220-241 (1992).
15. S.R. GRACE, B.S. LALLI, Oscillation theorems for second order superlinear differential equations with damping, J. Austral. Math. Soc. A 53, 156-165 (1992).
16. P. HARTMAN, Ordinary Differential Equations ,Wiley, New York, 1964.
17. J.W. HEIDEL, Uniqueness, continuation and nonoscillation for a second order nonlinear differential equation, Pacif. J. Math. 32, 3, 715-721 (1970).
18. I.T.KIGURADZE, T.A.CHANTURIA, Asymptotic properties of solutions of nonautonomous ordinary differential equations, Kluwer Acad. Publ., Dordrecht, 1993.
19. M.K. KWONG, J.S.W. WONG, Linear̀ization of second order nonlinear oscillation theorems, Trans. Amer. Mat. Soc. 279, 2, 705-721 (1983).
20. A. LOMTATIDZE, Oscillation and nonoscillation of Emden-Fowler type equation of second order, Arch. Math. Brno 32, 181-193 (1996).
21. W.E. MAHFOUD, S.H. RANKIN, Some properties of solutions of (r(t)ψ(x)xPrime)Prime + a(t)f(x) = 0 , SIAM J. Math. Anal. 10, 1, 49-54 (1979).
22. Z. NEHARI, Oscillation criteria for second-order linear differential equations, Trans. Amer. Mat. Soc. 85, 428-445 (1957).
23. G.G. PHILOS, Oscillation criteria for second order superlinear differential equations, Can. J. Math. XLI, 2, 321-340 (1989).
24. G.G. PHILOS, I.K. PURNARAS, On the oscillation of second order nonlinear differential equations, Arch. Math. 59, 260-271 (1992).
25. C.A. SWANSON, Comparison and oscillation theory of linear differential equations,Academic Press, New York, 1968.
26. W.F. TRENCH, Canonical forms and principal systems for general disconjugate equations, Trans. Amer. Math. Soc. 189, 319-327 (1974).
27. J.S.W. WONG, A note on second order nonlinear oscillation, SIAM Rev. 10, 1, 88-91 (1968).
28. J.S.W. WONG, Oscillations theorems for second order nonlinear differential equations, Bull. Inst. Math. Acad. Sinica 3, 283-309 (1975).
29. J.S.W. WONG, On the generalized Emden-Fowler equation, SIAM Rev. 17, 2, 339-360 (1975).
30. J.S.W. WONG, Remarks on nonoscillation Theorems for a second order nonlinear differential equation, Proc. Amer. Math. Soc. 83, 1, 541-546 (1981).
31. J.S.W. WONG, An oscillation criterion for second order nonlinear differential equations with iterated integral averages, Diff. Integr. Equat. 6, 1, 83-91 (1993).
32. J.S.W. WONG, C.C. YEH, An oscillation criterion for second order sublinear differential equations, J. Math. Anal. Appl. 171, 346-351 (1992).
33. Y.H. YU, M.Z. JIN, Oscillation theorems for a second order nonlinear differential equation, Appl. Math. Mech. 13, 4, 379-385 (1992) (English Ed.)