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February 2021 Multiple solutions for the fractional $p$-Laplacian equation with Hardy–Sobolev exponents
Chunyan Zhang, Jihui Zhang
Rocky Mountain J. Math. 51(1): 363-374 (February 2021). DOI: 10.1216/rmj.2021.51.363

Abstract

We study the fractional p-Laplacian problem with Hardy–Sobolev exponents. We prove: there is a λ0>0 such that for any λ(0,λ0), the above problem possesses infinitely many solutions. We achieve our goal by making use of variational methods, more specifically, the Nehari manifold and Lusternik–Schnirelmann theory.

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Chunyan Zhang. Jihui Zhang. "Multiple solutions for the fractional $p$-Laplacian equation with Hardy–Sobolev exponents." Rocky Mountain J. Math. 51 (1) 363 - 374, February 2021. https://doi.org/10.1216/rmj.2021.51.363

Information

Received: 23 December 2019; Revised: 10 June 2020; Accepted: 11 June 2020; Published: February 2021
First available in Project Euclid: 28 May 2021

Digital Object Identifier: 10.1216/rmj.2021.51.363

Subjects:
Primary: 58E05 , 58E30 , 58J37 , 58K05 , 65NXX

Keywords: fractional $p$-laplacian‎ , Hardy–Sobolev exponent , multiplicity of solutions , variational methods

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 1 • February 2021
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