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2010 Oscillation for Certain Nonlinear Neutral Partial Differential Equations
Quanwen Lin, Rongkun Zhuang
Int. J. Differ. Equ. 2010: 1-12 (2010). DOI: 10.1155/2010/619142

Abstract

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, where Ω is a bounded domain in the Euclidean N-space RN with a piecewise smooth boundary Ω and Δ is the Laplacian in RN. 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.

Citation

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Quanwen Lin. Rongkun Zhuang. "Oscillation for Certain Nonlinear Neutral Partial Differential Equations." Int. J. Differ. Equ. 2010 1 - 12, 2010. https://doi.org/10.1155/2010/619142

Information

Received: 29 April 2010; Accepted: 16 August 2010; Published: 2010
First available in Project Euclid: 26 January 2017

zbMATH: 1227.35025
MathSciNet: MR2727999
Digital Object Identifier: 10.1155/2010/619142

Rights: Copyright © 2010 Hindawi

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