Hartman-Wintner type theorem for PDE with p-Laplacian

R. Marik, Mendel University, Brno, Czech Republic

E. J. Qualitative Theory of Diff. Equ., Proc. 6'th Coll. Qualitative Theory of Diff. Equ., No. 18. (2000), pp. 1-7.

Abstract: The well known Hartman-Wintner oscillation criterion is extended to the PDE
$$div(||\nabla u||^{p-2}\nabla u)+c(x)|u|^{p-2}u=0\quad p>1\eqno{(E)}$$
The condition on the function $c(x)$ under which (E) has no solution positive for large $||x||$, i.e. $\infty$ belongs to the closure of the set of zeros of every solution defined on the domain $\Omega=\{x\in R^n: ||x||>1\}$, is derived.

You can download the full text of this paper in DVI, PostScript or PDF format, or have a look at the Zentralblatt or the Mathematical Reviews entry of this paper.