Spectrum of the fractional p-Laplacian in RN and decay estimate for positive solutions of a Schrödinger equation

Spectrum of the fractional p-Laplacian in RN and decay estimate for positive solutions of a Schrödinger equation

In this paper, we prove the existence of unbounded sequence of eigenvalues for the fractional p−Laplacian with weight in RN. We also show a nonexistence result when the weight has positive integral. In addition, we show some qualitative properties of the first eigenfunction including a sharp decay e...

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Bibliographic Details
Published in:Nonlinear analysis Vol. 193; p. 1
Main Authors: Del Pezzo, Leandro M., Quaas, Alexander
Format: Journal Article
Language:English
Published: Elmsford Elsevier Ltd 01-04-2020
Elsevier BV
Subjects:
Decay
Decay estimate
Eigenvalues
Eigenvectors
Fractional [formula omitted]-Laplacian
Schrodinger equation
Spectrum
Weight
Decay estimate
Fractional p-Laplacian
Spectrum
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Summary:In this paper, we prove the existence of unbounded sequence of eigenvalues for the fractional p−Laplacian with weight in RN. We also show a nonexistence result when the weight has 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.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2019.03.002