Some Abstract Critical Point Theorems and Applications in Wave Equations

Abstract

With the index defined in [J. Differential Equations, 2016, 260(4): 3749–3784] and [Front. Math., 2023, 18(3): 731–742], we get some critical point theorems for abstract operator equation without compactness assumption. As applications, we consider the periodic solutions of wave equations.

Keywords

Relative Morse index / periodic solutions / wave equations

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