## International Journal of Differential Equations

### Oscillation for Certain Nonlinear Neutral Partial Differential Equations

#### Abstract

We present some new oscillation criteria for second-order neutral partial functional differential equations of the form $(\partial /\partial t)\{p(t)(\partial /\partial t)[u(x,t)+{\sum }_{i=1}^{l}{\lambda }_{i}(t)u(x,t-{\tau }_{i})]\}=a(t)\Delta u(x,t)+{\sum }_{k=1}^{s}{a}_{k}(t)\Delta u(x,t-{\rho }_{k}(t))-q(x,t)f(u(x,t))-{\sum }_{j=1}^{m}{q}_{j}(x,t){f}_{j}(u(x,t-{\sigma }_{j}))$, $(x,t)\in \Omega \times{R}^{+}\equiv G$, where $\Omega$ is a bounded domain in the Euclidean $N$-space ${R}^{N}$ with a piecewise smooth boundary $\partial \Omega$ and $\Delta$ is the Laplacian in ${R}^{N}$. 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
Accepted: 16 August 2010
First available in Project Euclid: 26 January 2017

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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