International Journal of Differential Equations

Oscillation for Certain Nonlinear Neutral Partial Differential Equations

Quanwen Lin and Rongkun Zhuang

Full-text: Open access

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.

Article information

Source
Int. J. Differ. Equ., Volume 2010 (2010), Article ID 619142, 12 pages.

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

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1485399925

Digital Object Identifier
doi:10.1155/2010/619142

Mathematical Reviews number (MathSciNet)
MR2727999

Zentralblatt MATH identifier
1227.35025

Citation

Lin, Quanwen; Zhuang, Rongkun. Oscillation for Certain Nonlinear Neutral Partial Differential Equations. Int. J. Differ. Equ. 2010 (2010), Article ID 619142, 12 pages. doi:10.1155/2010/619142. https://projecteuclid.org/euclid.ijde/1485399925


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