Multiple Solutions for an Equation of Kirchhoff Type: Theoretical and Numerical Aspects - Martinez, André Luís Machado; Castelani, Emerson Vitor; Bressan, Glaucia Maria; Stiegelmeier, Elenice Weber (Trends in Computational and Applied Mathematics, 2018)
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.