Glasnik Matematicki, Vol. 40, No.2 (2005), 249-259.
UNSTABLE NEUTRAL DIFFERENTIAL EQUATIONS INVOLVING THE MAXIMUM FUNCTION
Guang Zhang and Malgorzata Migda
Department of Mathematics, Qingdao Technological University,
11, Fushun Road, Qingdao 266033, P. R. China
Institute of Mathematics, Faculty of Electrical Engineering,
Poznan University of Technology, Piotrowo 3a, 60-965 Poznan, Poland
Abstract. A nonlinear differential equation involving the maximum function
is studied. The existence and asymptotic behavior of
nonoscillatory solutions are considered. The difference between
the positive and negative solutions is illustrated by some
examples. Oscillation of solutions is also studied.
2000 Mathematics Subject Classification.
Key words and phrases. Differential equation, maximum function,
nonoscillation, oscillation, asymptotic property.
Full text (PDF) (free access)
- E. P. Popov,
Automatic Regulation and Control, Nauka, Moscow, 1966.
- D. Bainov, V. Petrov and V. Proicheva,
Oscillation of neutral differential equations with "maxima",
Revista Math. 8(1) (1995), 171-180.
- B. G. Zhang and G. Zhang,
Qualitative properties of functional differential equations with "maxima",
Rocky Mountain J. Math. 29(1) (1999), 357-367.
- B. G. Zhang and S. S. Cheng,
Asymptotic stability of nonoscillatory solutions of nonlinear neutral differential
equations involving the maximum function,
International J. Applied Math. 7 (1999), 771-779.
- L. H. Erbe, Q. Kong and B. G. Zhang,
Oscillation Theory for Functional Differential Equations,
Marcel Dekker, Inc., New York, 1995.
- I. Gyori and G. Ladas,
Oscillation Theory of Delay
Differential Equations with Applications, Clarendon Press, Oxford, 1991.
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