Geodesic
Inequalities for eigenfunctions of the $p$-Laplacian
Problemy analiza, Tome 2 (2013) no. 1, pp. 14-37

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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.
Keywords: eigenfunctions of $p$-Laplacian; $\sin_p$; generalized trigonometric function. 
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B. A. Bhayo; M. Vuorinen. Inequalities for eigenfunctions of the $p$-Laplacian. Problemy analiza, Tome 2 (2013) no. 1, pp. 14-37. http://geodesic.mathdoc.fr/item/PA_2013_2_1_a1/