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.



Titolo: Subharmonic solutions of the prescribed curvature equation
Autori: 
CORSATO, CHIARA
OMARI, PIERPAOLO
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Data di pubblicazione: 2016
Rivista: 
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS  
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.
Handle: http://hdl.handle.net/11368/2830905
Digital Object Identifier (DOI): http://dx.doi.org/10.1142/S021919971550042X
URL: http://www.worldscientific.com/doi/10.1142/S021919971550042X
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