scholarly journals Asymptotic behavior of nonoscillatory solutions of a higher order functional differential equation

1981 ◽  
Vol 24 (1) ◽  
pp. 85-92 ◽  
Author(s):  
Hiroshi Onose
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Nonoscillatory Solutions ◽  
Nonlinear Functional ◽  
Functional Differential ◽  
Approach Zero ◽  
Image Position

The asymptotic behavior of nonoscillatory solutions of nth order nonlinear functional differential equationsis investigated. Sufficient conditions are provided which ensure that all nonoscillatory solutions approach zero as t → ∞.

Asymptotic Behavior for Nonoscillatory Solutions of Second Order Nonlinear Functional Differential Equation

2012 ◽  
Vol 616-618 ◽  
pp. 2137-2141
Author(s):  
Zhi Min Luo ◽  
Bei Fei Chen
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Nonoscillatory Solutions ◽  
Nonlinear Functional ◽  
Nonlinear Functional Differential Equation ◽  
Functional Differential

This paper studied the asymptotic behavior of a class of nonlinear functional differential equations by using the Bellman-Bihari inequality. We obtain results which extend and complement those in references. The results indicate that all non-oscillatory continuable solutions of equation are asymptotic to at+b as under some sufficient conditions, where a,b are real constants. An example is provided to illustrate the application of the results.

scholarly journals Asymptotic behavior of nonoscillatory solutions of second order functional differential equations

1975 ◽  
Vol 13 (2) ◽  
pp. 291-299 ◽  
Author(s):  
Takaŝi Kusano ◽  
Hiroshi Onose
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Nonoscillatory Solutions ◽  
Oscillatory Solutions ◽  
Functional Differential ◽  
Approach Zero ◽  
Image Position

The asymptotic behavior of nonoscillatory solutions of the second order functional differential equationis studied. First, in the case when a(t)is oscillatory, sufficient conditions are given in order that all bounded non-oscillatory solutions of (*) approach zero as t → ∞. Secondly, in the case when a(t) is nonnegative, conditions are provided under which all nonoscillatory solutions of (*) tend to zero as t → ∞.

scholarly journals Oscillation of a functional differential equation arising from an industrial problem

1978 ◽  
Vol 26 (3) ◽  
pp. 323-329 ◽  
Author(s):  
Hiroshi Onose
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
First Order ◽  
Functional Differential ◽  
Image Position ◽  
Industrial Problem

AbstractIn the last few years, the oscillatory behavior of functional differential equations has been investigated by many authors. But much less is known about the first-order functional differential equations. Recently, Tomaras (1975b) considered the functional differential equation and gave very interesting results on this problem, namely the sufficient conditions for its solutions to oscillate. The purpose of this paper is to extend and improve them, by examining the more general functional differential equation

scholarly journals Asymptotic behavior of solutions of nonlinear functional differential equations

1994 ◽  
Vol 17 (4) ◽  
pp. 703-712
Author(s):  
Jong Soo Jung ◽  
Jong Yeoul Park ◽  
Hong Jae Kang
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Maximal Monotone Operator ◽  
Functional Differential Equations ◽  
Maximal Monotone ◽  
Asymptotic Behavior Of Solutions ◽  
Nonlinear Functional ◽  
Functional Differential

Using the properties of almost nonexpansive curves introduced by B. Djafari Rouhani, we study the asymptotic behavior of solutions of nonlinear functional differential equationdu(t)/dt+Au(t)+G(u)(t)?f(t), whereAis a maximal monotone operator in a Hilbert spaceH,f?L1(0,8:H)andG:C([0,8):D(A)¯)?L1(0,8:H)is a given mapping.

scholarly journals Nonoscillation theorems for functional differential equations of arbitrary order

1984 ◽  
Vol 7 (2) ◽  
pp. 249-256 ◽  
Author(s):  
John R. Graef ◽  
Myron K. Grammatikopoulos ◽  
Yuichi Kitamura ◽  
Takasi Kusano ◽  
Hiroshi Onose ◽  
...  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Arbitrary Order ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Solutions ◽  
Nonlinear Functional ◽  
Functional Differential ◽  
Nonoscillation Theorem

The authors give sufficient conditions for all oscillatory solutions of a sublinear forced higher order nonlinear functional differential equation to converge to zero. They then prove a nonoscillation theorem for such equations. A few intermediate results are also obtained.

scholarly journals A nonoscillation theorem for a second order sublinear retarded differential equation

1976 ◽  
Vol 15 (3) ◽  
pp. 401-406 ◽  
Author(s):  
Takaŝi Kusano ◽  
Hiroshi Onose
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Nonlinear Functional ◽  
Retarded Differential Equation ◽  
All Solutions ◽  
Functional Differential ◽  
Nonoscillation Theorem

Sufficient conditions are obtained for all solutions of a class of second order nonlinear functional differential equations to be nonoscillatory.

Oscillatory and Asymptotic Behavior of Third-Order Nonlinear Functional Differential Equations

2013 ◽  
Vol 303-306 ◽  
pp. 1247-1251
Author(s):  
Li Gao ◽  
Yuan Hong Yu ◽  
Quan Xin Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Third Order ◽  
Nonlinear Functional ◽  
Integral Averaging Technique ◽  
Generalized Riccati Transformation ◽  
Functional Differential

This paper is concerned with oscillatory and asymptotic behavior of solutions of a class of third-order nonlinear functional differential equations. By using the generalized Riccati transformation and the integral averaging technique, two new sufficient conditions which insure that the solution is oscillatory or converges to zero are established. The results obtained essentially generalize and improve earlier ones.

Periodic solutions to functional differential equations

1985 ◽  
Vol 101 (3-4) ◽  
pp. 253-271 ◽  
Author(s):  
O. A. Arino ◽  
T. A. Burton ◽  
J. R. Haddock
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Uniform Boundedness ◽  
Continuous Functions ◽  
Ultimate Boundedness ◽  
Space Of Continuous Functions ◽  
Uniform Ultimate Boundedness ◽  
Functional Differential ◽  
Image Position

SynopsisWe consider a system of functional differential equationswhere G: R × B → Rn is T periodic in t and B is a certain phase space of continuous functions that map (−∞, 0[ into Rn. The concepts of B-uniform boundedness and B-uniform ultimate boundedness are introduced, and sufficient conditions are given for the existence of a T-periodic solution to (1.1). Several examples are given to illustrate the main theorem.

On nonlinear boundary value problems for higher order functional differential equations

2016 ◽  
Vol 23 (4) ◽  
pp. 537-550 ◽  
Author(s):  
Ivan Kiguradze ◽  
Zaza Sokhadze
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Nonlocal Boundary ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Functional ◽  
Functional Differential

AbstractFor higher order nonlinear functional differential equations, sufficient conditions for the solvability and unique solvability of some nonlinear nonlocal boundary value problems are established.

Sign in / Sign up

Export Citation Format

Share Document