## On the oscillation of nonlinear two-dimensional differential systems

HTML articles powered by AMS MathViewer

- by I.-G. E. Kordonis and Ch. G. Philos PDF
- Proc. Amer. Math. Soc.
**126**(1998), 1661-1667 Request permission

## 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.## References

- Saunders MacLane,
*Steinitz field towers for modular fields*, Trans. Amer. Math. Soc.**46**(1939), 23–45. MR**17**, DOI 10.1090/S0002-9947-1939-0000017-3 - Štefan Belohorec,
*Non-linear oscillations of a certain non-linear second-order differential equation*, Mat.-Fyz. Časopis. Sloven. Akad. Vied.**12**(1962), 253–262 (Slovak, with English summary). MR**159994** - W. J. Coles,
*Oscillation criteria for nonlinear second order equations*, Ann. Mat. Pura Appl. (4)**82**(1969), 123–133. MR**255907**, DOI 10.1007/BF02410793 - Man Kam Kwong and James S. W. Wong,
*An application of integral inequality to second order nonlinear oscillation*, J. Differential Equations**46**(1982), no. 1, 63–77. MR**677584**, DOI 10.1016/0022-0396(82)90110-3 - Man Kam Kwong and James S. W. Wong,
*Oscillation of Emden-Fowler systems*, Differential Integral Equations**1**(1988), no. 2, 133–141. MR**922556** - D. D. Mirzov,
*The oscillatoriness of the solutions of a system of nonlinear differential equations*, Differencial′nye Uravnenija**9**(1973), 581–583, 592 (Russian). MR**0315209** - D. D. Mirzov,
*On the question of the oscillation of the solutions of a system of nonlinear differential equations*, Mat. Zametki**16**(1974), 571–576 (Russian). MR**374562** - D. D. Mirzov,
*The oscillatory nature of the solutions of a nonlinear differential system of Emden-Fowler type*, Differentsial′nye Uravneniya**16**(1980), no. 11, 1980–1984, 2108 (Russian). MR**599428** - Paul Waltman,
*An oscillation criterion for a nonlinear second order equation*, J. Math. Anal. Appl.**10**(1965), 439–441. MR**173050**, DOI 10.1016/0022-247X(65)90138-1 - James S. W. Wong,
*On two theorems of Waltman*, SIAM J. Appl. Math.**14**(1966), 724–728. MR**206409**, DOI 10.1137/0114061 - James S. W. Wong,
*Oscillation theorems for second order nonlinear differential equations*, Proc. Amer. Math. Soc.**106**(1989), no. 4, 1069–1077. MR**952324**, DOI 10.1090/S0002-9939-1989-0952324-2 - James S. W. Wong,
*Oscillation criteria for second order nonlinear differential equations with integrable coefficients*, Proc. Amer. Math. Soc.**115**(1992), no. 2, 389–395. MR**1086346**, DOI 10.1090/S0002-9939-1992-1086346-0

## 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
- Received by editor(s): September 23, 1996
- Communicated by: Hal L. Smith
- © Copyright 1998 American Mathematical Society
- 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