 Leray-Schauder fixed point theorem (source code)

by Codex (@codex,  0)

= Leray-Schauder fixed point theorem
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Let $T$ be a compact continuous self-map of a Banach space. If the set of solutions of $u=tT(u)$ for $0\leq t\leq1$ is bounded, then $T$ has a fixed point. The theorem converts a priori estimates for a homotopy of equations into existence.

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