Multiple Solutions for a Sixth Order Boundary Value Problem

André Luís Machado Martinez, Cristiane Aparecida Pendeza Martinez, Glaucia Maria Bressan, Roberto Molina de Souza, Elenice Weber Stiegelmeier

Abstract


This work presents conditions for the existence of multiple solutions for a sixth order equation with homogeneous boundary conditions using Avery Peterson's theorem. In addition, non-trivial examples are presented and a new numerical method based on the Banach's Contraction Principle is introduced.

Keywords


numerical solutions, sixth-order, boundary value problem and multiple solutions

Full Text:

PDF

References


M. M. ADJUSTOVS and A. J. LEPINS, “Extremal solutions of a boundaryvalue problem for a sixthorder equation,” Differ. Equ., vol. 50, no. 2, pp. 141–146, 2014.

R. P. AGARWAL, B. KOVACS, and D. O’REGAN, “Positive solutions for

a sixth-order boundary value problem with four parameters,” Bound. Value

Probl., no. 2, pp. 184–205, 2013.

R. P. AGARWAL, B. KOVACS, and D. O’REGAN, “Existence of positive

solution for a sixth-order differential system with variable parameters,” J. Appl.Math. Comput., no. 1-2, pp. 437–454, 2014.

T. GARBUZA, “On solutions of one 6-th order nonlinear boundary value problem,” Math. Model. Anal., vol. 13, no. 3, pp. 349–355, 2008.

W. W. SUQIN GE and Q. YANG, “Dependence of eigenvalues of sixth-order boundary value problems on the boundary,” Bull. Aust. Math. Soc., vol. 90, no. 3, pp. 457–468, 2014.

K. GHANBARI and H. MIRZAEI, “On the isospectral sixth order sturmliouville equation,” J. Lie Theory, vol. 23, no. 4, pp. 921–935, 2013.

J. R. GRAEF and B. YANG, “Boundary value problems for sixth order nonlinear ordinary differential equations,” Dynam. Systems Appl., vol. 10, no. 4, pp. 465–475, 2001.

T. GYULOV, “Trivial and nontrivial solutions of a boundary value problem for a sixth-order ordinary differential equation,” C. R. Acad. Bulgare Sci., vol. 9, no. 58, pp. 1013–1018, 2005.

M. MOLLER and Â. B. ZINSOU, “Sixth order differential operators with eigenvalue dependent boundary conditions,” Appl. Anal. Discrete Math., vol. 2, no. 7, pp. 378–389, 2013.

J. V. CHAPAROVA, L. A. PELETIER, S. A. T. F. GENG, and Y. YE, “Existence and nonexistence of nontrivial solutions of semilinear sixth-order ordinary differential equations,” Appl. Math. Lett., vol. 17, no. 10, pp. 1207–1212, 2004.

B. YANG, “POSITIVE SOLUTIONS TO A NONLINEAR SIXTH ORDER BOUNDARY VALUE PROBLEM,” Differential Equations Applications,

vol. 11, no. 2, pp. 307–317, 2019.

A. L. M. MARTINEZ, E. V. CASTELANI, and R. HOTO, “Solving a second order m-point boundary value problem,” Nonlinear Studies, vol. 26, no. 1, pp. 15–26, 2018.

A. L. M. MARTINEZ, E. V. CASTELANI, G. M. BRESSAN, and E. W. STIEGELMEIER, “Multiple Solutions for an Equation of Kirchhoff Type: Theoretical and Numerical Aspects,” Trends in Applied and Computational Mathematics, vol. 19, no. 3, pp. 559–572, 2018.

C. A. PENDEZA MARTINEZ, A. L. M. MARTINEZ, G. M. BRESSAN, E. V. CASTELANI, and R. M. de SOUZA, “Multiple solutions for a fourth order equation with nonlinear boundary conditions: theoretical and numerical aspects,” Differential Equations Applications, vol. 11, no. 3, pp. 335–348, 2019.




DOI: https://doi.org/10.5540/tema.2021.022.01.1-12

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM

Refbacks

  • There are currently no refbacks.



Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

Indexed in:

                        

 

Desenvolvido por:

Logomarca da Lepidus Tecnologia