Generalized elliptic functions and their application to a nonlinear eigenvalue problem with $p$-Laplacian

Details Generalized elliptic functions and their application to a nonlinear eigenvalue problem with $p$-Laplacian Generalized elliptic functions and their application to a nonlinear eigenvalue problem with $p$-Laplacian

2010-01-03

arxiv.org/abs/1001.0377v2

Mathematics

Analysis of PDEs

17 pages

Scientific paper

The Jacobian elliptic functions are generalized and applied to a nonlinear eigenvalue problem with $p$-Laplacian. The eigenvalue and the corresponding eigenfunction are represented in terms of common parameters, and a complete description of the spectra and a closed form representation of the corresponding eigenfunctions are obtained. As a by-product of the representation, it turns out that a kind of solution is also a solution of another eigenvalue problem with $p/2$-Laplacian.

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