Hiroshi Onose

A comparison theorem and the forced oscillation

Consider the n -th order delay differential equation In the last few years, the oscillatory behavior of delay differential equations has been the subject of intensive investigations. But much less is known about the equation (A) with small forcing term q ( t ). The only papers devoted to this problem are by Kartsatos, Kusano, and the present author. The purpose of this paper is to prove some new oscillation theorems which contain the previous results.

Oscillation of a functional differential equation arising from an industrial problem

In 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

A comparison method for forced oscillations

Consider the functional differential equations (1)x(n)(t)+a(t)f(x(g(t)))=Q(t) and (2)x(n)(t)+s(t)f(x(t))=0 wheres(t)≧γa(t) for all sufficiently larget, sayt≧T>0 and for some γ, 0<γ<1. Recently,E. D. True proposed a new comparison theorem for equations (1) and (2) with which he proved some results on the oscillation of (1). The purpose of the present paper is to extend them to the more general case. The examples indicate that the results are applicable to interesting problems.

Asymptotic behavior of nonoscillatory solutions of nonlinear differential equations with forcing term

SuntoIn questo lavoro si studiano il comportamento asintotico delle soluzioni non oscillatorie di una classe di equazioni differenziali di ordine superiore al secondo. In particolare, si dánno condizioni sufficienti perchè tutte le soluzioni, non oscillatorie e limitate, dell’equazione considerata, abbiano per limite lo zero quando la variabile indipendente tende all’infinito.

Nonoscillation theorems for functional differential equations of arbitrary order

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.

Nonlinear oscillation of fourth order functional differential equations

SummaryIn the oscillation theory of nonlinear differential equations one of the important problems is to find necessary and sufficient conditions for the equations under consideration to be oscillatory. Beginning with the pionearing work of F. V. Atkinson, there have been a number of papers. Recently, Kusano and Naito proved the interesting results to the jourth order nonlinear ordinary differential equations of the from [r(t)y″(t)]″+y(t)F(y(t)2,t)=0. In the present paper, we will extend them to the more general functional differential equations and improve the not clear parts of them. Also, we will propose a new simple definition of nonlinearity of the functional differential equations.