APPROXIMATION AND RAPID CONVERGENCE OF SOLUTIONS FOR PERIODIC NONLINEAR PROBLEMS

We study existence and approximation of solutions of some second order nonlinear periodic boundary value problem of the type

                            −x''(t) = f(t, x, x' ),      t ∈ [0, T],

                               x(0) = x(T),  x'(0) = x'(T),

in the presence of lower and upper solutions. We develop the upper and lower solutions method and the quasilinearization technique for the existence and approximation of solutions. We apply our theoretical results to a medical problem.