Glasnik Matematicki, Vol. 40, No.2 (2005), 249-259.

UNSTABLE NEUTRAL DIFFERENTIAL EQUATIONS INVOLVING THE MAXIMUM FUNCTION

Guang Zhang and Malgorzata Migda

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.

DOI: 10.3336/gm.40.2.06

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