  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.
