Complex sentence: He is known for his basic work on topological methods in the calculus of variations, leading to establish powerful tools aimed at establishing the existence of solutions to variational problems when classical direct methods of the calculus of variations cannot be applied.
Split into simpler sentences: He is known for his basic work on topological methods in the calculus of variations. These provide tools aimed at establishing the existence of solutions to variational problems when classical direct methods of the calculus of variations cannot be applied.