Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 28, pp. 1-10.
Title: Oscillation criteria for a class of nonlinear partial differential
equations
Author: Robert Marik (Mendel Univ., Czech Republic)
Abstract:
This paper presents sufficient conditions on the function $c(x)$
to ensure that every solution of partial differential equation
$$
\sum_{i=1}^{n}{\partial \over \partial x_i}
\Phi_{p}({\partial u \over \partial x_i})+B(x,u)=0, \quad
\Phi_p(u):=|u|^{p-1}\mathop{\rm sgn} u. \quad p>1
$$
is weakly oscillatory, i.e. has zero outside of every ball in
$\mathbb{R}^n$. The main tool is modified Riccati technique
developed for Schrodinger operator by Noussair and Swanson [11].
Submitted May 24, 2001. Published March 8, 2002.
Math Subject Classifications: 35B05
Key Words: Oscillation criteria; nonlinear oscillation; unbounded domains.