The monotonicity of the period function for planar Hamiltonian vector fields

AbstractIf the Hamiltonian system with Hamiltonian H(x, y) = 12y2 + V(x) has a center at the origin it is shown that the period function for the family of periodic trajectories surrounding the center is monotone when the function V(V′)2 is convex. This theorem is applied to determine existence and uniqueness of solutions for the Neumann boundary value problem X″ = a(x′)2 + bx + c, x′(0) = x′(1) = 0