Solution of a BVP constrained in an infinitely deep potential well
Solution of a BVP constrained in an infinitely deep potential well
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.
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.
Boundary value problems for linear higher-order PDEs, Variational methods applied to PDEs, existence, dual action principle, potential well
Boundary value problems for linear higher-order PDEs, Variational methods applied to PDEs, existence, dual action principle, potential well
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