Generalized Jacobian elliptic functions and their application to bifurcation problems associated with p-Laplacian

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40 Citations (Scopus)

Abstract

The Jacobian elliptic functions are generalized and applied to bifurcation problems associated with p-Laplacian. The values of bifurcation parameter and the corresponding solutions are represented in terms of common parameters, and a complete description of the bifurcation diagram and a closed form representation of the corresponding solutions are obtained. As a by-product of the representation, it turns out that a kind of solution is also a solution of an eigenvalue problem of p/2-Laplacian.

Original languageEnglish
Pages (from-to)24-35
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Volume385
Issue number1
DOIs
Publication statusPublished - 2012 Jan 1

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Bifurcation (mathematics)
Byproducts

Keywords

  • Bifurcation problem
  • Eigenvalue problem
  • Jacobian elliptic functions
  • P-Laplacian

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

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AB - The Jacobian elliptic functions are generalized and applied to bifurcation problems associated with p-Laplacian. The values of bifurcation parameter and the corresponding solutions are represented in terms of common parameters, and a complete description of the bifurcation diagram and a closed form representation of the corresponding solutions are obtained. As a by-product of the representation, it turns out that a kind of solution is also a solution of an eigenvalue problem of p/2-Laplacian.

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