Constructive analysis of periodic solutions with interval halving
András Rontó, Miklós I. Rontó, Nataliya Shchobak · Boundary Value Problems · 2013
For a constructive analysis of the periodic boundary value problem for systems of non-linear non-autonomous ordinary differential equations, a numerical-analytic approach is developed, which allows one to both study the solvability and construct approximations to the solution.An interval halving technique, by using which one can weaken significantly the conditions required to guarantee the convergence, is introduced.The main assumption on the equation is that the non-linearity is locally Lipschitzian.An existence theorem based on properties of approximations is proved.A relation to Mawhin's continuation theorem is indicated.