Periodic solutions of some nonlinear autonomous functional differential equations
- 234 Downloads
We develop here some new fixed point theorems and apply them to the question of existence of nontrivial periodic solutions of nonlinear, autonomous functional differential equations. We prove that the standard results of G. S. Jones and R. B. Grafton can be obtained by our methods, and we prove periodicity results for some equations, for instance a neutral functional differential equation, which appear inaccessible by previous techniques.
KeywordsDifferential Equation Periodic Solution Point Theorem Fixed Point Theorem Standard Result
- R. B. Grafton,Liénard equations with delay: existence and stability of periodic solutions, Abstract of talk at the Park City, Utah, Symposium on Functional Differential Equations, March 1972.Google Scholar
- J. Kaplan - J. Yorke,On the stability of a periodic solution of a differential-delay equation, to appear.Google Scholar