Electron. J. Diff. Eqns., Vol. 2002(2002), No. 28, pp. 1-10.

Oscillation criteria for a class of nonlinear partial differential equations

Robert Marik

Abstract:
This paper presents sufficient conditions on the function $c(x)$ to ensure that every solution of partial differential equation
$$ \sum_{i=1}^{n}{\partial \over \partial x_i} \Phi_{p}({\partial u \over \partial x_i})+B(x,u)=0, \quad \Phi_p(u):=|u|^{p-1}\mathop{\rm sgn} u. \quad p greater than 1 $$
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.

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Robert Marik
Dept. of Mathematics, Mendel University
Zemedelska 3
613 00 Brno, Czech Republic
e-mail: marik@mendelu.cz

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