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 conditions. We present the result for the existence of multiple solutions based on the Avery-Peterson fixed-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 determine multiple solutions to the problem addressed. (2010): 34-XX, 34-BXX, 34-B15. Mathematics subject classification

Multiple Solutions for a Sixth Order Boundary Value Problem

“…Even so, we performed a test to verify the behavior of Algorithm 1 in an attempt to determine multiple solutions. So inspired by the works [10], [9] and [11], how know that the solutions we are looking for must be continuous and satisfy the condition 0.2. We choose initial approaches that satisfy the conditions u(0) = u (0) = 0 and u (1) = 0.…”