Generalizing the Lusternik–Schnirelmann critical point theorem
Generalizing the Lusternik–Schnirelmann critical point theorem
In this paper, the author obtains the multiplicity of critical points of a continuously differentiable functional $\varphi:\mathcal{V}\times D\longrightarrow\mathbb{R}$, defined on the product of an $N$-dimensional compact manifold $\mathcal{V}$ of class $C^{2}$ without boundary and an $M$-dimensional convex compact set $D$ with nonempty interior. Moreover, he extends this result to an infinite-dimensional setting and applies it to the existence of periodic solutions of pendulum equations.
- University of Trieste Italy
cup length, multiple critical points, Critical point theory, pendulum equation, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, Lusternik-Schnirelmann, Periodic solutions to ordinary differential equations, Lusternik-Schnirelmann category, Critical point theory; Lusternik-Schnirelmann
cup length, multiple critical points, Critical point theory, pendulum equation, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, Lusternik-Schnirelmann, Periodic solutions to ordinary differential equations, Lusternik-Schnirelmann category, Critical point theory; Lusternik-Schnirelmann
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