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D. Georgiou, K. Kreith (1985)
Functional Characteristic Initial Value ProblemsJ. Math. Anal. Appl., 107
D.P. Mishev, D.D. Bainov (1988)
Oscillation of the Solutions of Parabolic Differential Equations of Neutral TypeAppl. Math. Comput., 28
Junjie Wei (1988)
Oscillation of Second Order Delay Differential EquationsAnn. Diff. Eqs., 4
D.P Mishev, D.D. Bainov (1986)
Oscillation Properties of the Solutions of a Class of Hyperbolic Equations of Neutral TypeFunkcialaj Ekvacioj, 29
N. Yoshida (1987)
Forced Oscillations of Solutions of Parabolic EquationsBull. Austral. Math. Soc., 36
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 ----
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Jul 13, 2005
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