Si dimostra l'esistenza di una soluzione per il problema al contorno
\[
-\ddot{x}=\nabla U(x),x(0)=x(a)=0
\]
dove x:$\left[0,a\right]\mathbf{R^{\textrm{n}},}U:\Omega\subset\mathbf{R^{\textrm{n}}\rightarrow\mathbf{R}}$,
U convessa e U(x)$\rightarrow+\infty$quando x$\rightarrow\text{\ensuremath{\partial}}\Omega$.
Il metodo usato sì basa sul Principio di Azione Duale di Clarke e
Ekeland. We prove existence of a solution for the boundary value problem
\[
-\ddot{x}=\nabla U(x),x(0)=x(a)=0
\]
where x:$\left[0,a\right]\mathbf{R^{\textrm{n}},}U:\Omega\subset\mathbf{R^{\textrm{n}}\rightarrow\mathbf{R}}$,
U convex and U(x)$\rightarrow+\infty$ as x$\rightarrow\text{\ensuremath{\partial}}\Omega$.
The method employed is based on the use ot the Dual Action Principle
of Clarke and Ekeland.
