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


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.   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


  1. E. P. Popov, Automatic Regulation and Control, Nauka, Moscow, 1966.

  2. D. Bainov, V. Petrov and V. Proicheva, Oscillation of neutral differential equations with "maxima", Revista Math. 8(1) (1995), 171-180.

  3. B. G. Zhang and G. Zhang, Qualitative properties of functional differential equations with "maxima", Rocky Mountain J. Math. 29(1) (1999), 357-367.

  4. 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.

  5. L. H. Erbe, Q. Kong and B. G. Zhang, Oscillation Theory for Functional Differential Equations, Marcel Dekker, Inc., New York, 1995.

  6. I. Gyori and G. Ladas, Oscillation Theory of Delay Differential Equations with Applications, Clarendon Press, Oxford, 1991.

Glasnik Matematicki Home Page