An iterative method for a second order problem with nonlinear two-point boundary conditions
Amster, Pablo | 2012-11-08
A semi-linear second order ODE under a nonlinear two-point boundary condition is considered.
Under appropriate conditions on the nonlinear term of the equation, we define a two-dimensional
shooting argument which allows to obtain solutions for some specific situations by the use of
Poincar´e-Miranda’s theorem. Finally, we apply this result combined with the method of upper
and lower solutions and develop an iterative sequence that converges to a solution of the problem.