Electron. J. Diff. Eqns., Vol. 2004(2004), No. 60, pp. 1-25.

Some metric-singular properties of the graph of solutions of the one-dimensional p-Laplacian

Mervan Pasic & Vesna Zupanovic

Abstract:
We study the asymptotic behaviour of $epsilon$-neighbourhood of the graph of a type of rapidly oscillating continuous functions. Next, we estate necessary and sufficient conditions for rapid oscillations of solutions of the main equation. This enables us to verify some new singular properties of bounded continuous solutions of a class of nonlinear p-Laplacian by calculating lower and upper bounds for the Minkowski content and the $s$-dimensional density of the graph of each solution and its derivative.

Submitted October 28, 2003. Published April 19, 2004.
Math Subject Classifications: 35J60, 34B15, 28A75.
Key Words: Nonlinear p-Laplacian, bounded solutions, qualitative properties, graph, singularity, Minkowski content, s-dimensional density.

Show me the PDF file (404K), TEX file, and other files for this article.

Mervan Pasic
Department of Mathematics
Faculty of Electrical Engineering and Computing
University of Zagreb
Unska 3, 10000 Zagreb, Croatia
email: mervan.pasic@fer.hr
Vesna Zupanovic
Department of Mathematics
Faculty of Electrical Engineering and Computing
University of Zagreb
Unska 3, 10000 Zagreb, Croatia
email: vesna.zupanovic@fer.hr

Return to the EJDE web page