Matemáticas Enseñanza Universitaria

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An iterative method for a second order problem with nonlinear two-point boundary conditions.
(2012-11-08) Amster, Pablo; Cárdenas Alzate, Pedro Pablo
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.
Acceso abierto
Sturm-Liouville boundary conditions for a second order ODE.
(2011-10-13) Amster, Pablo; Cárdenas, Pedro P.
We study the semilinear second order ODE u00 + g(t, u) = 0 under the following Sturm- Liouville boundary condition au(0) + bu0(0) = u0 and cu(T) + du0(T) = uT . We obtain solutions by topological methods. Moreover, we show that a solution may be constructed recursively, under appropriate conditions.