Monotone solutions of a higher-order neutral differential equation

• Autorzy: Zhang, G. , Migda, M.
• Języki publikacji: EN

Abstrakty

EN

A continuous function x(t) is said to be (*)-monotone with a positive number τ if x(t) > 0 and (-1)ⁿ(x(t) - x(t - τ))⁽ⁿ⁾ ≥ 0 for n ≥ 0. This paper is concerned with various classifications of (*)-monotone solutions of a neutral differential eąuation. Necessary and/or sufficient conditions are then derived for the existence of these solutions.

Słowa kluczowe

EN

neutral differential equation; existence criteria; (*)-monotone solution; asymptotic behavior

• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2004
• Tom: Vol. 44, nr 1
• Strony: 147--162
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Zhang, G.

• Department of Mathematics, Qingdao Institute of Architecture and Engineering, Qingdao, Shandong 266033, P.R.China,

autor

Migda, M.

• Department of Mathematics, Poznań University of Technology, Piotrowo 3a, 60-965 Poznań, Poland,

Bibliografia

• [1] M. P. Chen, J. S. Yu and L. H. Huang, Oscillations of first order neutral differential equations with variable coefficients, J. Math. Anal. Appl. 185 (1994), 288-301.
• [2] S. S. Cheng, Oscillation theorems for fourth-order differential and difference equations, Proceedings of the International Conference on Functional Differential Equations, Publishing House of the Electronic Industry, Guangzhou, China, (1993), 37-46.
• [3] S. S. Cheng and J. Yan, Monotone solutions of n-th order linear differential equations, Diff. Eq. Dynamical Systems 3 (1995), 15-22.
• [4] S. S. Cheng and G. Zhang, Monotone solutions of a higher-order neutral difference equation, Georgian Math. J. 5 (1998), 49-54.
• [5] L. Erbe, Hille-Wintner type comparison theorem for self-adjoint fourth order linear differential equations, Proc. Amer. Math. Soc. 80 (1980), 417-422.
• [6] L. H. Erbe, Q. Kong and B. G. Zhang, Oscillation Theory for Functional Differential Equations, Marcel Dekker, Inc., 1995.
• [7] K. Gopalsamy, B. S. Lalli and B. G. Zhang, Oscillation of odd-order neutral differential eąuations, Czechoslovak Math. J. 42 (1992), 313-323.
• [8] I. T. Kiguradze, On the oscillatory and monotone solutions of ordinary differential equations , Arch. Math. (Brno) 14 (1978), 21-44.
• [9] W. J. Kim, Monotone and oscillatory solutions of y(n) + p y = 0, Proc. Amer. Math. Soc. 62 (1977), 77-82.
• [10] B. Yang and B. G. Zhang, Qualitative analysis of a class of neutral differential equations, Funkcialaj Ekvacioj 39 (1996), 347-362.
• [11] G. Zhang and S. S. Cheng, On a functional differential equation related to the Emden-Fowler equation, Functional Differential Equations 4 (1997), 215-221.
• [12] B. G. Zhang and J. S. Yu, The existence of positive solutions of neutral differential equations, Sci. Sinica 8 (1992), 785-790.