A class of nonlinear differential equations of second order in time
Résumé
In this paper, $\phi$ will denote a lower semicontinuous convex proper function from $\mathbb{R}^N = H$ to $\mathbb{R}\cup\{+\infty\}$. The effective domain of $\phi$ is the set dom $\phi=\{x\in\mathbb{R}^N | \phi(x)<+ \infty\}$. We shall suppose that the interior of dom $\phi$ in $\mathbb{R}^N$ is not empty, and $\phi\geq 0$. These two assumptions do not restrict the generality. The scalar product in $H$ is denoted by $(x,y)$.
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