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Remarks on dispersive estimates and curvature
Periodic solutions of a periodic scalar piecewise ode
1. | Departamento de Enseñanzas Básicas de la Ingeniería Naval, Universidad Politécnica de Madrid, Escuela Técnica Superior de Ingenieros Navales, 28040 Madrid, Spain |
2. | Departamento de Matemáticas, Universidad de Extremadura, Facultad de Ciencias, 06071 Badajoz, Spain |
3. | Departamento de Matemáticas, Universidad de Los Andes, Facultad de Ciencias, 5101 Mérida, Venezuela |
We find that the solutions are $\mathcal C^1$-functions when the equation restricted to the equatorial line has a finite number of zeroes. Moreover, if $f$ and $g$ are analytic functions and the zeroes on the equatorial line are finite and simple, the set of periodic solutions consists of isolated periodic solutions and a finite number (determined by the number of zeroes) of closed "bands" of periodic solutions.
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