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

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.