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

Authors

  • André Luís Machado Martinez Universidade Tecnológica Federal do Paraná https://orcid.org/0000-0003-1888-648X
  • Emerson Vitor Castelani Universidade Estadual de Maringá
  • Glaucia Maria Bressan Universidade Tecnológica Federal do Paraná
  • Elenice Weber Stiegelmeier

DOI:

https://doi.org/10.5540/tema.2018.019.03.559

Keywords:

Multiple solution, Kirchhoff Equation, numerical solutions

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.

Author Biographies

André Luís Machado Martinez, Universidade Tecnológica Federal do Paraná

Departamento Acadêmico de Matemática

Emerson Vitor Castelani, Universidade Estadual de Maringá

Department of Mathematics, DMA

References

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Published

2018-12-17

How to Cite

Martinez, A. L. M., Castelani, E. V., Bressan, G. M., & Stiegelmeier, E. W. (2018). Multiple Solutions for an Equation of Kirchhoff Type: Theoretical and Numerical Aspects. Trends in Computational and Applied Mathematics, 19(3), 559. https://doi.org/10.5540/tema.2018.019.03.559

Issue

Vol. 19 No. 3 (2018)

Section

Original Article

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