Resumen de Monotonicity of the period map of a non-Hamiltonian center

Jorge Billeke, Eduardo Sáez

• In this paper we prove that the period map of $$\ddot{x}- ax\thinspace\dot{x} + x^3 = 0,\quad with\quad a^2 < 8 ,$$ is monotonically decreasing. As an application, it is obtained that the respective Dirichlet boundary problem for two points has either a unique solution or no solution at all while the Neumann boundary value problem has a unique solution.