| Abstract: |
| Jacobi elliptic functions are natural extensions of trigonometric functions and play an important role in expressing exact solutions to certain semilinear ordinary differential equations. In this talk, we introduce a generalization of the Jacobi elliptic functions by replacing certain constants with three parameters (besides the modulus) and investigate their fundamental properties. This class of functions also extends the generalized trigonometric functions introduced by Dr\`{a}bek and Man\`{a}sevich, and is well suited for the study of certain quasilinear ordinary differential equations involving the $p$-Laplacian. We derive differential equations and integral formulas satisfied by the generalized Jacobi elliptic functions, together with binomial-type inequalities of Edmunds--Lang type. If time permits, we also discuss a generalization of Legendre`s relation for their periods, namely, generalized complete elliptic integrals. |
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