On the oscillation of nonlinear

two-dimensional differential systems

Authors:
I.-G. E. Kordonis and Ch. G. Philos

Journal:
Proc. Amer. Math. Soc. **126** (1998), 1661-1667

MSC (1991):
Primary 34C10

DOI:
https://doi.org/10.1090/S0002-9939-98-04503-1

MathSciNet review:
1458253

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: An oscillation criterion is given for a certain form of nonlinear two-dimensional differential systems. This criterion originated in a well-known oscillation result due to Coles (as extended and improved by Wong) concerning second order nonlinear differential equations with alternating coefficients.

**1.**F. V. Atkinson,*On second order nonlinear oscillation*, Pacific J. Math.**5**(1955), 643-647. MR**17:264e****2.**S. Belohorec,*Oscillatory solutions of certain nonlinear differential equations of second order*, Mat. Fyz. Casopis Sloven Akad. Vied.**11**(1961), 250-255. MR**28:3208****3.**W. J. Coles,*Oscillation criteria for nonlinear second order equations*, Ann. Mat. Pura Appl.**82**(1969), 123-134. MR**41:567****4.**M. K. Kwong and J. S. W. Wong,*An application of integral inequality to second order nonlinear oscillation*, J. Differential Equations**46**(1982), 63-77. MR**84g:34059****5.**M. K. Kwong and J. S. W. Wong,*Oscillation of Emden-Fowler systems*, Differential Integral Equations**1**(1988), 133-141. MR**89b:34075****6.**D. D. Mirzov,*Oscillatory properties of solutions of a system of nonlinear differential equations*, Differentsial'nye Uravneniya**9**(1973), 581-583; English transl., Differential Equations**9**(1973), 447-449. MR**47:3758****7.**D. D. Mirzov,*The oscillation of solutions of a system of nonlinear differential equations*, Mat. Zametki**16**(1974), 571-576; English transl., Math. Notes**16**(1974), 932-935. MR**51:10762****8.**D. D. Mirzov,*Oscillation properties of solutions of a nonlinear Emden-Fowler differential system*, Differentsial'nye Uravneniya**16**(1980), 1980-1984; English transl., Differential Equations**16**(1980), 1260-1263. MR**82a:34046****9.**P. Waltman,*An oscillation criterion for a nonlinear second order equation*, J. Math. Anal. Appl.**10**(1965), 439-441. MR**30:3265****10.**J. S. W. Wong,*On two theorems of Waltman*, SIAM J. Appl. Math.**14**(1966), 724-728. MR**34:6228****11.**J. S. W. Wong,*Oscillation theorems for second order nonlinear differential equations*, Proc. Amer. Math. Soc.**106**(1989), 1069-1077. MR**89m:34042****12.**J. S. W. Wong,*Oscillation criteria for second order nonlinear differential equations with integrable coefficients*, Proc. Amer. Math. Soc.**115**(1992), 389-395. MR**92i:34042**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
34C10

Retrieve articles in all journals with MSC (1991): 34C10

Additional Information

**I.-G. E. Kordonis**

Affiliation:
Department of Mathematics University of Ioannina 451 10 Ioannina, Greece

Email:
cphilos@cc.uoi.gr

**Ch. G. Philos**

Affiliation:
Department of Mathematics University of Ioannina 451 10 Ioannina, Greece

DOI:
https://doi.org/10.1090/S0002-9939-98-04503-1

Keywords:
Differential system,
solution,
oscillation

Received by editor(s):
September 23, 1996

Communicated by:
Hal L. Smith

Article copyright:
© Copyright 1998
American Mathematical Society