scholarly journals Distributional and entire solutions of ordinary differential and functional differential equations

1983 ◽  
Vol 6 (2) ◽  
pp. 243-269 ◽  
Author(s):  
S. M. Shah ◽  
Joseph Wiener
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Integral Equations ◽  
Linear Equations ◽  
Functional Differential Equations ◽  
Generalized Function ◽  
Entire Solutions ◽  
Polynomial Coefficients ◽  
Functional Differential

A brief survey of recent results on distributional and entire solutions of ordinary differential equations (ODE) and functional differential equations (FDE) is given. Emphasis is made on linear equations with polynomial coefficients. Some work on generalized-function solutions of integral equations is also mentioned.

scholarly journals Distributional and entire solutions of linear functional differential equations

1982 ◽  
Vol 5 (4) ◽  
pp. 729-736 ◽  
Author(s):  
Joseph Wiener
Keyword(s):  
Differential Equations ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Generalized Function ◽  
Unified Approach ◽  
Entire Solutions ◽  
Polynomial Coefficients ◽  
Functional Differential

A unified approach to the study of generalized-function and entire solutions to linear functional differential equations with polynomial coefficients is suggested.

scholarly journals Approximation methods and the generalised Fuller index for semi-flows in Banach spaces

1986 ◽  
Vol 29 (3) ◽  
pp. 299-308 ◽  
Author(s):  
A. J. B. Potter
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Banach Spaces ◽  
Functional Differential Equations ◽  
Periodic Points ◽  
Approximation Methods ◽  
Functional Differential ◽  
Linear Differential ◽  
Fuller Index

In [3] Fuller introduced an index (now called the Fuller index) in order to study periodic solutions of ordinary differential equations. The objective of this paper is to give a simple generalisation of the Fuller index which can be used to study periodic points of flows in Banach spaces. We do not claim any significant breakthrough but merely suggest that the simplistic approach, presented here, might prove useful for the study of non-linear differential equations. We show our results can be used to study functional differential equations.

scholarly journals Oscillation for Certain Nonlinear Neutral Partial Differential Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-12
Author(s):  
Quanwen Lin ◽  
Rongkun Zhuang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Smooth Boundary ◽  
Functional Differential Equations ◽  
Second Order ◽  
Piecewise Smooth Boundary ◽  
Linear Ordinary Differential Equations ◽  
Partial Functional Differential Equations ◽  
Functional Differential

We present some new oscillation criteria for second-order neutral partial functional differential equations of the form(∂/∂t){p(t)(∂/∂t)[u(x,t)+∑i=1lλi(t)u(x,t-τi)]}=a(t)Δu(x,t)+∑k=1sak(t)Δu(x,t-ρk(t))-q(x,t)f(u(x,t))-∑j=1mqj(x,t)fj(u(x,t-σj)),(x,t)∈Ω×R+≡G, whereΩis a bounded domain in the EuclideanN-spaceRNwith a piecewise smooth boundary∂ΩandΔis the Laplacian inRN. Our results improve some known results and show that the oscillation of some second-order linear ordinary differential equations implies the oscillation of relevant nonlinear neutral partial functional differential equations.

scholarly journals Ultimate Boundedness of the Systems Governed by Stochastic Differential Equations

1972 ◽  
Vol 47 ◽  
pp. 111-144 ◽  
Author(s):  
Yoshio Miyahara
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stochastic Differential Equations ◽  
Functional Differential Equations ◽  
Ultimate Boundedness ◽  
Functional Differential ◽  
The Stability

The stability of the systems given by ordinary differential equations or functional-differential equations has been studied by many mathematicians. The most powerful tool in this field seems to be the Liapunov’s second method (see, for example [6]).

scholarly journals General Decay Stability for Stochastic Functional Differential Equations with Infinite Delay

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Yue Liu ◽  
Xuejing Meng ◽  
Fuke Wu
Keyword(s):  
Differential Equations ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
General Decay ◽  
Stochastic Functional Differential Equations ◽  
General Decay Rate ◽  
Polynomial Coefficients ◽  
Functional Differential ◽  
The Stability ◽  
Stochastic Functional

So far there are not many results on the stability for stochastic functional differential equations with infinite delay. The main aim of this paper is to establish some new criteria on the stability with general decay rate for stochastic functional differential equations with infinite delay. To illustrate the applications of our theories clearly, this paper also examines a scalar infinite delay stochastic functional differential equations with polynomial coefficients.

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