Critical points with lack of compactness and singular dynamical systems (Q1101749)

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.