We provide a multiplicity result for critical points of a functional defined on the product of a compact manifold without boundary and a convex set, by assuming, for example, an avoiding rays condition at the boundary of that set. We then extend this result to an infinite-dimensional setting which well applies to the search of periodic solutions of pendulum-like equations.
Generalizing the Lusternik–Schnirelmann critical point theorem
Fonda, Alessandro
2019-01-01
Abstract
We provide a multiplicity result for critical points of a functional defined on the product of a compact manifold without boundary and a convex set, by assuming, for example, an avoiding rays condition at the boundary of that set. We then extend this result to an infinite-dimensional setting which well applies to the search of periodic solutions of pendulum-like equations.File in questo prodotto:
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