ON BERNOULLI BOUNDARY VALUE PROBLEM

We consider the boundary value problem: {x((m))(t) = f (t, (x) over bar( t)), a <= t <= b, m > 1 x(a) = beta(0) Delta x((k)) equivalent to x((k))( b)-x((k))(a) = beta(k+1), k = 0,..., m-2 where (x) over bar (t) = (x(t), x'(t),...., x((m-1))(t)), beta(i) is an element of R, i = 0,..., m-1, and f is continuous at least in the interior of the domain of interest. We give a constructive proof of the existence and uniqueness of the solution, under certain conditions, by Picard's iteration. Moreover Newton's iteration method is considered for the numerical computation of the solution.