On non-linear boundary value problems containing parameters

Miklos Ronto

Address. Institute of Mathematics, University of Miskolc, H-3515 Miskolc-Egyetemvaros, Hungary

E-mail: matronto@gold.uni-miskolc.hu

Abstract. We consider a boundary value problem containing two parameters both in the non-linear ordinary differential equation and in the non-linear boundary conditions. By using a suitable change of variables, we bring the given problem to a family of those with linear boundary conditions (plus some non-linear determining equations), and apply an iterative method to approximately find its solution.

AMSclassification. 34B10

Keywords. Parametrised boundary value problems, non-linear boundary conditions, numerical-analytic methods, successive approximation, determining equations