The asymptotic behavior for neutral stochastic partial functional differential equations

2017 ◽  
Vol 35 (6) ◽  
pp. 1060-1083 ◽  
Author(s):  
Huabin Chen
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Partial Functional Differential Equations ◽  
Functional Differential

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 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.

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