Numerical method of bicharacteristics for hyperbolic partial functional differential equations

CALCOLO ◽  
2009 ◽  
Vol 46 (1) ◽  
pp. 1-24 ◽  
Author(s):  
Wojciech Czernous
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Functional Differential Equations ◽  
Partial Functional Differential Equations ◽  
Functional Differential

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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