Multiple Solutions for Lagrangian Systems in T Superscript n
Abstract
This paper studies existence of multiple periodic solutions of a general Lagrangean system having as a configuration space the n-dimensional torus T raised to the n power. The critical points of the potential energy correspond to equilibrium of the system when no external forces are present. The author studies the number of T-periodic solutions of the system, inherited by the equilibrium solutions, when the external force is not zero. In particular it is proven that the forced system has at least the same number of periodic solutions as critical points the potential has, when certain condition is satisfied. The proof of the results are based of the notion of Ljusternik- Schnirelmann relative category. The author relates the level sets of the potential with the level sets of the functional associated to the Lagrangean system. He also applies the ideas developed to study some multiplicity result for the existence of solutions of an elliptic partial difference equation with Neumann boundary condition.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 10, 1989
- Accession Number
- ADA210646
Entities
People
- Patricio L. Felmer
Organizations
- University of Wisconsin–Madison