Periodic solutions of some second order differential systems
The existence of a non-trivial periodic solution for the autonomous Rayleigh equation is proved, assuming conditions which do not imply that has a definite sign for large. A similar result is obtained for the periodically forced equation .
A criterion for the existance of periodic solutions of an ordinary differential equation of order k proved by J. Andres and J. Vorâcek for k = 3 is extended to an arbitrary odd k.
Si dimostra un teorema di esistenza di soluzioni periodiche dell'equazione differenziale ordinaria del terzo ordine con le funzioni , , periodiche in di periodo .
We prove the existence and conditional stability of periodic solutions to semilinear evolution equations of the form u̇ = A(t)u + g(t,u(t)), where the operator-valued function t ↦ A(t) is 1-periodic, and the operator g(t,x) is 1-periodic with respect to t for each fixed x and satisfies the φ-Lipschitz condition ||g(t,x₁) - g(t,x₂)|| ≤ φ(t)||x₁-x₂|| for φ(t) being a real and positive function which belongs to an admissible function space. We then apply the results to study the existence, uniqueness...
A classical mechanics Lagrangian system with even Lagrangian is considered. The configuration space is a cylinder . A large class of nonhomotopic periodic solutions has been found.