Multiple solutions for a fourth order equation with nonlinear boundary conditions: theoretical and numerical aspects

Abstract

. We consider in this work the fourth order equation with nonlinear boundary condi- tions. We present the result for the existence of multiple solutions based on the Avery-Peterson fi xed-point theorem. This work is also a study for numerical solutions based on the Levenberg- Maquardt method with a heuristic strategy for initial points that proposes to numerically deter-mine multiple solutions to the problem addressed.