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Oscillation of solutions of hyperbolic equations of neutral type

Oscillation of solutions of hyperbolic equations of neutral type Vol.lO No.1 ACTA MATHEMATICAE APPLICATAE SINICA Jan., 1994 Study Bulletin OSCILLATION OF SOLUTIONS OF HYPERBOLIC EQUATIONS OF NEUTRAL TYPE" YU YUANttONG ('~.ff.Jb~-) ( lm~it.te o, f Applit.d Mat.~matica, the Chines= Ac, adcmg o/ 8¢iem:ea, Bei~'ng 100080, C~'n,=) cuI B.,,o'ro~G (~'¢'R) { Bia.#~a Normal Coilqe, Bin=~o= ~$6604, China) In the last few years there was much interest in studying the oscillatory behavior of solutions of partial differential equations with deviating arguments. We refer the reader to Mishev and Bainov [1, 2], Yoshida [3] and Georgiou & Kreith [4]. However, only the paper [1] considers the oscillation of solutions of hyperbolic equations of neutral type. The purpose of this paper is to obtain the sufficient conditions for the oscillation of the solutions of hyperbolic equations of neutral type of the form 6 2 at~ [ '~(~' t) + p(t)=(=, t - ,-)] =a(t)Au(z, t) - q((:).f(u(z, o'(t))), (z, t) Efl x R+ -- G, (1) where R+ = [0, co), n is a bounded domain in R ~ With a piecewise smooth boundary an. Suppose that the following conditions (A) hold: (A1) a(t) is a continuous function in R+ such that limt-.oo a(t) -- 0% a(t) _< t and f ---- http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Oscillation of solutions of hyperbolic equations of neutral type

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References (5)

Publisher
Springer Journals
Copyright
Copyright © 1994 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02006263
Publisher site
See Article on Publisher Site

Abstract

Vol.lO No.1 ACTA MATHEMATICAE APPLICATAE SINICA Jan., 1994 Study Bulletin OSCILLATION OF SOLUTIONS OF HYPERBOLIC EQUATIONS OF NEUTRAL TYPE" YU YUANttONG ('~.ff.Jb~-) ( lm~it.te o, f Applit.d Mat.~matica, the Chines= Ac, adcmg o/ 8¢iem:ea, Bei~'ng 100080, C~'n,=) cuI B.,,o'ro~G (~'¢'R) { Bia.#~a Normal Coilqe, Bin=~o= ~$6604, China) In the last few years there was much interest in studying the oscillatory behavior of solutions of partial differential equations with deviating arguments. We refer the reader to Mishev and Bainov [1, 2], Yoshida [3] and Georgiou & Kreith [4]. However, only the paper [1] considers the oscillation of solutions of hyperbolic equations of neutral type. The purpose of this paper is to obtain the sufficient conditions for the oscillation of the solutions of hyperbolic equations of neutral type of the form 6 2 at~ [ '~(~' t) + p(t)=(=, t - ,-)] =a(t)Au(z, t) - q((:).f(u(z, o'(t))), (z, t) Efl x R+ -- G, (1) where R+ = [0, co), n is a bounded domain in R ~ With a piecewise smooth boundary an. Suppose that the following conditions (A) hold: (A1) a(t) is a continuous function in R+ such that limt-.oo a(t) -- 0% a(t) _< t and f ----

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 13, 2005

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