Multiple Solutions for an Equation of Kirchhoff Type: Theoretical and Numerical Aspects

Abstract

A nonlinear boundary value problem related to an equation of Kirchhoff type is considered. The existence of multiple positive solutions is proved through Avery-Peterson Fixed Point Theorem. A numerical method based on Levenberg-Marquadt algorithm combined with a heuristic process is present in order to align numerical and theoretical aspects.

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.…”