Periodic boudary-value problem for Hill's equation in the case of parametric resonance

Necessary and sufficient conditions for the existence of solutions of nonlinear nonautonomous periodic problem for Hills equation in the case of parametric resonance. A characteristic feature of the task is the need of finding, as desired solution, and the corresponding eigenfunction, which ensures solvability of the periodic problem for Hills equation in the case of parametric resonance. To construct solutions of the periodic problem for Hills equation and the corresponding eigenfunction in the case of parametric resonance proposed iterative scheme, based on the method of simple iterations with used list-square technics.