Geodesic
Rectifiability of solutions of the one-dimensional \(p\)-Laplacian
Electronic journal of differential equations, Tome 2005 (2005)
In the recent papers [8] and [10] a class of Caratheodory functions $f(t,\eta ,\xi )$ rapidly sign-changing near the boundary point $t=a$, has been constructed so that the equation $-(|y'|^{p-2}y')'=f(t,y,y')$ in $(a,b)$ admits continuous bounded solutions $y$ whose graphs $G(y)$ do not possess a finite length. In this paper, the same class of functions $-(|y'|^{p-2}y')'=f(t,y,y')$ will be given, but with slightly different input data compared to those from the previous papers, such that the graph $G(y)$ of each solution $y$ is a rectifiable curve in $\mathbb{R}^{2}$. Moreover, there is a positive constant which does not depend on $y$ so that .
Classification : 35J60, 34B15, 28A75
Keywords: nonlinear p-Laplacian, bounded continuous solutions, graph, qualitative properties, length, rectifiability 
@article{EJDE_2005__2005__a72,
     author = {Pasic,  Mervan},
     title = {Rectifiability of solutions of the one-dimensional {\(p\)-Laplacian}},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1129.35402},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a72/}
}
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Pasic,  Mervan. Rectifiability of solutions of the one-dimensional \(p\)-Laplacian. Electronic journal of differential equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a72/