This is a preview of subscription content, log in via an institution to check access.
References
G. J. Butler, The existence of continuable solutions of a second order differential equation. Canad. J. Math.29, 472–479 (1977).
G. J. Butler, Integral averages and the oscillation of second order differential equations. SIAM J. Math. Anal.11, 190–200 (1980).
G. J. Butler andL. H. Erbe. A generalization of Olech-Opial-Wazewski oscillation criteria to second order nonlinear equations. Nonlinear Anal.11, 207–219 (1987).
G. J. Butler, L. H. Erbe andA. B. Mingarelli, Riccati techniques and variational principles in oscillation theory for linear systems. Trans. Amer. Math. Soc.303, 263–282 (1987).
W. J. Coles, An oscillation criterion for second-order linear differential equations. Proc. Amer. Math. Soc.19, 755–759 (1968).
P. Hartman, On nonoscillatory linear differential equations of second order. Amer. J. Math.74, 389–400 (1952).
P.Hartman, Ordinary Differential Equations. New York, 1964.
I. V. Kamenev, Certain specifically nonlinear oscillation theorems (Russian). Mat. Zametki10, 129–134 (1971). Engl. Transi. Math. Notes10, 502–505 (1971).
I. V. Kamenev, Oscillation criteria related to averaging of solutions of ordinary differential equations of second order (Russian). Differentsial'nye Uravneniya10, 246–252 (1974). Engl. Transl. Differential Equations10, 179–183 (1974).
I. V. Kamenev, An integral criterion for oscillation of linear differential equations of second order (Russian). Mat. Zametki23, 249–251 (1978). Engl. Transl. Math. Notes23, 136–138 (1978).
T. Kura, Oscillation theorems for a second order sublinear ordinary differential equation. Proc. Amer. Math. Soc.84, 535–538 (1982).
M. K. Kwong andJ. S. W. Wong, On an oscillation theorem of Belohorec. SIAM J. Math. Anal.14, 474–476 (1983).
M. K. Kwong andJ. S. W. Wong, On the oscillation and nonoscillation of second order sublinear equations. Proc. Amer. Math. Soc.85, 547–551 (1982).
M. K. Kwong andJ. S. W. Wong, Linearization of second-order nonlinear oscillation theorems. Trans. Amer. Math. Soc.279, 705–722 (1983).
M. K. Kwong andA. Zettl, Asymptotically constant functions and second order linear oscillation. J. Math. Anal. Appl.93, 475–494 (1983).
H. Onose, Oscillation criteria for second order nonlinear differential equations. Proc. Amer. Math. Soc.51, 67–73 (1975).
H. Onose, On Butler's conjecture for oscillation of an ordinary differential equation. Quart. J. Math. Oxford Ser. (2)34, 235–239 (1983).
C. G. Philos, Oscillation of sublinear differential equations of second order. Nonlinear Anal.7, 1071–1080 (1983).
C. G. Philos, A second order superlinear oscillation criterion. Canad. Math. Bull.27, 102–112 (1984).
C. G. Philos, Integral averages and second order superlinear oscillation. Math. Nachr.120, 127–138 (1985).
C. G. Philos, On second order sublinear oscillation. Aequationes Math.27, 242–254 (1984).
C. G. Philos, Integral averaging techniques for the oscillation of second order sublinear ordinary differential equations. J. Austral. Math. Soc. Ser. A40, 111–130 (1986).
C. G. Philos, On the oscillation of second order sublinear ordinary differential equations with alternating coefficients. Math. Nachr.146, 105–116 (1990).
C. G. Philos, An oscillation criterion for superlinear differential equations of second order. J. Math. Anal. Appl.148, 306–316 (1990).
C. G. Philos, Oscillation criteria for second order superlinear differential equations. Canad. J. Math.41, 321–340 (1989).
C. G. Philos, Integral averages and oscillation of second order sublinear differential equations. Differential Integral Equations4, 205–213 (1991).
C. G. Philos andI. K. Purnaras, Oscillations in superlinear differential equations of second order. J. Math. Anal. Appl.165, 1–11 (1992).
D. Willett, On the oscillatory behavior of the solutions of second order linear differential equations. Ann. Polon. Math.21, 175–194 (1969).
D. Willett, Classification of second order linear differential equations with respect to oscillation. Adv. in Math.3, 594–623 (1969).
A. Wintner, A criterion of oscillatory stability. Quart. Appl. Math.7, 115–119 (1949).
J. S. W. Wong, On second order nonlinear oscillation. Funkcial. Ekvac.11, 207–234 (1969).
J. S. W. Wong, A second order nonlinear oscillation theorem. Proc. Amer. Math. Soc.40, 487–491 (1973).
J. S. W. Wong, Oscillation theorems for second order nonlinear differential equations. Bull. Inst. Math. Acad. Sinica3, 283–309 (1975).
J. S. W. Wong, On the generalized Emden-Fowler equation. SIAM Rev.17, 339–360 (1975).
J. S. W. Wong, An oscillation criterion for second order nonlinear differential equations. Proc. Amer. Math. Soc.98, 109–112 (1986).
J. S. W. Wong, An oscillation criterion for second order sublinear differential equations. Canad. Math. Soc. Conf. Proc.8, 299–302 (1987).
J. S. W. Wong, Oscillation theorems for second-order nonlinear differential equations. Proc. Amer. Math. Soc.106, 1069–1077 (1989).
J. S. W. Wong, An oscillation theorem for second order sublinear differential equations. Proc. Amer. Math. Soc.110, 633–637 (1990).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01197323