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EnglishWe discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential equation \begin{equation*} -\Big( u'/{ \sqrt{1-{u'}^2}}\Big)' = f(t,u). \end{equation*} Depending on the behaviour of $f=f(t,s)$ near $s=0$, we prove the existence of either one, or two, or three, or infinitely many positive solutions. In general, the positivity of $f$ is not required. All results are obtained by reduction to an equivalent non-singular problem to which variational or topological methods apply in a classical fashion.
| Titolo: | Positive solutions of the Dirichlet problem for the one-dimensional Minkowski-curvature equation |
| Autori: | |
| Data di pubblicazione: | 2012 |
| Rivista: | |
| Abstract: | We discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential equation \begin{equation*} -\Big( u'/{ \sqrt{1-{u'}^2}}\Big)' = f(t,u). \end{equation*} Depending on the behaviour of $f=f(t,s)$ near $s=0$, we prove the existence of either one, or two, or three, or infinitely many positive solutions. In general, the positivity of $f$ is not required. All results are obtained by reduction to an equivalent non-singular problem to which variational or topological methods apply in a classical fashion. |
| Handle: | http://hdl.handle.net/11368/2507945 |
| Appare nelle tipologie: | 1.1 Articolo in Rivista |
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