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arXiv · 1812.00925

Spectrum of the fractional $p-$Laplacian in $\mathbb{R}^N$ and decay estimate for positive solutions of a Schr\"odinger equation

Leandro M. Del Pezzo·Alexander Quaas
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Abstract

In this paper, we prove the existence of unbounded sequence of eigenvalues for the fractional $p-$Laplacian with weight in $\mathbb{R}^N.$ We also show a nonexistence result when the weighthas positive integral. In addition, we show some qualitative properties of the first eigenfunction including a sharp decay estimate. Finally, we extend the decay result to the positive solutions of a Schr\"odinger type equation.

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Leandro M. Del Pezzo, Alexander Quaas. 2018-12-03. Spectrum of the fractional $p-$Laplacian in $\mathbb{R}^N$ and decay estimate for positive solutions of a Schr\"odinger equation. https://doi.org/10.1016/j.na.2019.03.002

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