Trends in Computational and Applied Mathematics (Dec 2018)

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

  • André Luís Machado Martinez,
  • Emerson Vitor Castelani,
  • Glaucia Maria Bressan,
  • Elenice Weber Stiegelmeier

DOI
https://doi.org/10.5540/tema.2018.019.03.559
Journal volume & issue
Vol. 19, no. 3

Abstract

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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.

Keywords