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

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 Schrödinger type equation.

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References in corpus (2)

• A Hopf's lemma and a strong minimum principle for the fractional $p$-Laplacian
• Multiplicity and concentration results for some nonlinear Schrödinger equations with the fractional $p$-Laplacian

Cited by in corpus (4)

• The fractional $p$-biharmonic systems: optimal Poincaré constants, unique continuation and inverse problems
• Nonlocal planar Schrödinger-Poisson systems in the fractional Sobolev limiting case
• Concentration phenomena for fractional magnetic NLS equations
• Principal eigenvalue and positive solutions for Fractional $P-Q$ Laplace operator in quantum field theory