#### 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

*e-mail:* `dtguangzhang@yahoo.com.cn`
Institute of Mathematics, Faculty of Electrical Engineering,
Poznan University of Technology, Piotrowo 3a, 60-965 Poznan, Poland

*e-mail:* `mmigda@math.put.poznan.pl`

**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.**
34K15.

**Key words and phrases.** Differential equation, maximum function,
nonoscillation, oscillation, asymptotic property.

**Full text (PDF)** (free access)
DOI: 10.3336/gm.40.2.06

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