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

#### 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.
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http://www.worldscientific.com/doi/10.1142/S021919971550042X
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11368/2830905