MATHEMATICA BOHEMICA, Vol. 125, No. 2, pp. 199-213 (2000)

Asymptotic properties of solutions of second order quasilinear functional differential equations of neutral type

Takasi Kusano, Pavol Marusiak

T. Kusano, Department of Applied Mathematics, Fukuoka University, Fukuoka, 814-01, Japan, e-mail: tkusano@ssat.fukuoka-u.ac.jp.; P. Marusiak, Department of Applied Mathematics, Faculty of Science, University of Zilina, J. M. Hurbana 15, 010 26 Zilina, Slovak Republic, e-mail: marusiak@fpv.utc.sk

Abstract: This paper establishes existence of nonoscillatory solutions with specific asymptotic behaviors of second order quasilinear functional differential equations of neutral type. Then sufficient, sufficient and necessary conditions are proved under which every solution of the equation is either oscillatory or tends to zero as $ t \to \infty $.

Keywords: quasilinear differential equations of neutral type, oscillatory, non-oscillatory solutions, Schauder-Tychonoff fixed point theorem

Classification (MSC2000): 34K40, 34K25

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