Periodic motion in a class of nthorder autonomous differential equations
Abstract
Sufficient conditions are obtained for the existence of periodic motion in a class of autonomous nonlinear differential equations of order greater than two. The approach is based on the decomposition of an equation into a linear and a nonlinear part. The analysis relies on some basic ideas from linear analysis and geometry. Sufficient conditions for a periodic solution are derived by means of a general topological principle referred to as the torus principle. The existence of a periodic solution is concluded by an appropriate use of the Brouwer fixedpoint theorem.
 Publication:

Journal of Mathematical Analysis and Applications
 Pub Date:
 March 1976
 Bibcode:
 1976JMAA...53..669W
 Keywords:

 Differential Equations;
 Nonlinear Equations;
 Nonlinear Systems;
 Periodic Functions;
 Topology;
 Eigenvalues;
 Existence Theorems;
 Fixed Points (Mathematics);
 Invariance;
 Toruses;
 Physics (General)