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Nonlinear Boundary-value Problems with Multiple Solutions

In: Homotopy Analysis Method in Nonlinear Differential Equations

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  • Shijun Liao

    (Shanghai Jiao Tong University)

Abstract

In this chapter, using three different types of nonlinear boundary-value equations with multiple solutions, we verify the validity of the HAM-based Mathematica package BVPh (version 1.0) for nth-order nonlinear boundary-value equations F in a finite interval 0≤z≤a, subject to the n linear boundary conditions B, (1≤k≤n), where F is a nth-order nonlinear differential operator, F is a linear operator, γ k is a constant, respectively. Especially, the socalled multiple-solution-control parameter is introduced into initial guess in order to search for multiple solutions. We illustrate that, using the BVPh 1.0 as a tool, multiple solutions of some nonlinear boundary-value equations can be found out by means of such kind of multiple-solution-control parameter.

Suggested Citation

  • Shijun Liao, 2012. "Nonlinear Boundary-value Problems with Multiple Solutions," Springer Books, in: Homotopy Analysis Method in Nonlinear Differential Equations, chapter 0, pages 285-314, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-25132-0_8
    DOI: 10.1007/978-3-642-25132-0_8
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