Inequalities for eigenfunctions of the $p$-Laplacian

Mathematics – Classical Analysis and ODEs

Scientific paper

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19 pages

Scientific paper

Motivated by the work of P. Lindqvist, we study eigenfunctions of the
one-dimensional $p$-Laplace operator, the $\sin_p$ functions, and prove several
inequalities for these and $p$-analogues of other trigonometric functions and
their inverse functions. Similar inequalities are given also for the
$p$-analogues of the hyperbolic functions and their inverses.

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