We study the existence of subharmonic solutions of the prescribed curvature equation \begin{equation*} -\Big( u'/{ \sqrt{1+{u'}^2}}\Big)' = f(t,u). \end{equation*} According to the behaviour at zero, or at infinity, of the prescribed curvature $f$, we prove the existence of arbitrarily small classical subharmonic solutions, or bounded variation subharmonic solutions with arbitrarily large oscillations.
Subharmonic solutions of the prescribed curvature equation / Corsato, Chiara; Omari, Pierpaolo; Zanolin, Fabio. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - STAMPA. - 18:3(2016), pp. 1550042.1-1550042.33. [10.1142/S021919971550042X]
Subharmonic solutions of the prescribed curvature equation
CORSATO, CHIARA;OMARI, PIERPAOLO;
2016-01-01
Abstract
We study the existence of subharmonic solutions of the prescribed curvature equation \begin{equation*} -\Big( u'/{ \sqrt{1+{u'}^2}}\Big)' = f(t,u). \end{equation*} According to the behaviour at zero, or at infinity, of the prescribed curvature $f$, we prove the existence of arbitrarily small classical subharmonic solutions, or bounded variation subharmonic solutions with arbitrarily large oscillations.| File | Dimensione | Formato | |
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