In the recent papers  and  a class of Caratheodory functions rapidly sign-changing near the boundary point , has been constructed so that the equation in admits continuous bounded solutions whose graphs do not possess a finite length. In this paper, the same class of functions will be given, but with slightly different input data compared to those from the previous papers, such that the graph of each solution is a rectifiable curve in . Moreover, there is a positive constant which does not depend on so that .
Submitted November 11, 2004. Published April 24, 2005.
Math Subject Classifications: 35J60, 34B15, 28A75.
Key Words: Nonlinear p-Laplacian; bounded continuous solutions; graph; qualitative properties; length; rectifiability.
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| Mervan Pasic |
Department of Mathematics
Faculty of Electrical Engineering and Computing
University of Zagreb
Unska 3, 10000 Zagreb, Croatia
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