On non-linear boundary value problems containing parameters. (English) Zbl 1090.34519

Rontó, Miklós

Arch. Math., Brno 36, Suppl., 585-593 (2000).

The author considers a boundary value problem for nonlinear ordinary differential equation with two parameters involving both in the equation and in the nonlinear boundary conditions. By using a suitable substitution of variables he reduces the given problem to a family of those with linear boundary conditions and some nonlinear determining equations. Then he applies an iterative method to find an approximate solution of given problem.

Reviewer: Robert Hakl (Brno)

MSC:

34B10

Nonlocal and multipoint boundary value problems for ordinary differential equations

Keywords:

parametrised boundary value problems; non-linear boundary conditions; numerical-analytic methods; successive approximation; determining equations