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Types and criteria of nonoscillatory solutions for a class of second order neutral functional differential equations with nonpositive coefficients

Types and criteria of nonoscillatory solutions for a class of second order neutral functional... Vol.8 No.2 ACTA MATHEMATICAE APPLICATAE SINICA Apr., 1992 Study Bulletin TYPES AND CRITERIA OF NONOSCILLATORY SOLUTIONS FOR A CLASS OF SECOND ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NONPOSITIVE COEFFICIENTS" RUAN JIONG (~ ~l~) ( Fudan Uni.eraty, Shanghai P.OO4S& China) ( Shando~ Normal Univer~ty, Jinan gSO014, China) In this paper we discuss the types and criteria of nonosciUatory solutions for the fol- lowing second order neutral functional differential equation with nonpositive coefficients (b > ~)) (i) [~(0 - c(O~(t - ~)l" - p(t, ¢)~[9(t, ¢)]d~(O = o fa where r > O, c(t) E C 2, 0 < Ic(OI < 1, p(t,O > O, 9(t,¢) _< t, 9(t, ¢) is nondecreasing in both t and ~; a(~) is nondecreasing in ~, limt-.+oo g(t, ¢) --- +oo, ~ E [a, b]. The integral in (1) is a Stieltjes integral. There are some results on the asymptotic behavior of nonosciUatory solutions to the second order retarded functional differential equation with nonpositive coefficients, e.g., see [1 I. However ) it see'ms to us that little is known about the asymptotic behavior of nonoscillatory solutions for the second order neutral functional differential equation with nonpositive coefficients. In this paper four types of nonosci]latory solutions http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Types and criteria of nonoscillatory solutions for a class of second order neutral functional differential equations with nonpositive coefficients

Ruan, Jiong; Fu, Xilin
Acta Mathematicae Applicatae Sinica , Volume 8 (2) – Jul 13, 2005
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References (2)

Publisher
Springer Journals
Copyright
Copyright © 1992 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/BF02006153
Publisher site
See Article on Publisher Site

Abstract

Vol.8 No.2 ACTA MATHEMATICAE APPLICATAE SINICA Apr., 1992 Study Bulletin TYPES AND CRITERIA OF NONOSCILLATORY SOLUTIONS FOR A CLASS OF SECOND ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NONPOSITIVE COEFFICIENTS" RUAN JIONG (~ ~l~) ( Fudan Uni.eraty, Shanghai P.OO4S& China) ( Shando~ Normal Univer~ty, Jinan gSO014, China) In this paper we discuss the types and criteria of nonosciUatory solutions for the fol- lowing second order neutral functional differential equation with nonpositive coefficients (b > ~)) (i) [~(0 - c(O~(t - ~)l" - p(t, ¢)~[9(t, ¢)]d~(O = o fa where r > O, c(t) E C 2, 0 < Ic(OI < 1, p(t,O > O, 9(t,¢) _< t, 9(t, ¢) is nondecreasing in both t and ~; a(~) is nondecreasing in ~, limt-.+oo g(t, ¢) --- +oo, ~ E [a, b]. The integral in (1) is a Stieltjes integral. There are some results on the asymptotic behavior of nonosciUatory solutions to the second order retarded functional differential equation with nonpositive coefficients, e.g., see [1 I. However ) it see'ms to us that little is known about the asymptotic behavior of nonoscillatory solutions for the second order neutral functional differential equation with nonpositive coefficients. In this paper four types of nonosci]latory solutions

Journal

Acta Mathematicae Applicatae Sinica – Springer Journals

Published: Jul 13, 2005

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