Critical points with lack of compactness and singular dynamical systems. (English) Zbl 0642.58017

The existence of T-periodic solutions of n-dimensional dynamical systems like \(\dots y=-\text{grad} V(t,y)\) with a T-periodic potential V having singularities is established. That result is obtained by proving a theorem concerning the existence of critical points with lack of compactness. (The Palais-Smale condition does not hold!) The existence result for the critical points uses topological properties of level sets and Morse type arguments.
Reviewer: N.Jacob


58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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