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Advances in Nonlinear Analysis

Editor-in-Chief: Radulescu, Vicentiu / Squassina, Marco

IMPACT FACTOR 2018: 6.636

CiteScore 2018: 5.03

SCImago Journal Rank (SJR) 2018: 3.215
Source Normalized Impact per Paper (SNIP) 2018: 3.225

Mathematical Citation Quotient (MCQ) 2017: 1.89

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Existence and multiplicity of entire solutions for fractional p-Kirchhoff equations

Patrizia Pucci
  • Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, via Vanvitelli 1, 06123 Perugia, Italy
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/ Mingqi Xiang / Binlin Zhang
Published Online: 2015-09-16 | DOI: https://doi.org/10.1515/anona-2015-0102


The purpose of this paper is mainly to investigate the existence of entire solutions of the stationary Kirchhoff type equations driven by the fractional p-Laplacian operator in ℝN. By using variational methods and topological degree theory, we prove multiplicity results depending on a real parameter λ and under suitable general integrability properties of the ratio between some powers of the weights. Finally, existence of infinitely many pair of entire solutions is obtained by genus theory. Last but not least, the paper covers a main feature of Kirchhoff problems which is the fact that the Kirchhoff function M can be zero at zero. The results of this paper are new even for the standard stationary Kirchhoff equation involving the Laplace operator.

Keywords: Fractional p-Laplacian; Kirchhoff type equations; variational methods; multiple solutions

MSC: 35R11; 35A15; 35J60; 47G20

About the article

Received: 2015-07-28

Accepted: 2015-08-04

Published Online: 2015-09-16

Published in Print: 2016-02-01

Funding Source: MIUR

Award identifier / Grant number: Aspetti variazionali e perturbativi nei problemi differenziali nonlineari

Funding Source: INDAM-GNAMPA

Award identifier / Grant number: Prot_2015_000368

Funding Source: Fundamental Research Funds for the Central Universities

Award identifier / Grant number: 3122015L014

Funding Source: Natural Science Foundation of Heilongjiang Province of China

Award identifier / Grant number: A201306

Funding Source: Research Foundation of Heilongjiang Educational Committee

Award identifier / Grant number: 12541667

Funding Source: Doctoral Research Foundation of Heilongjiang Institute of Technology

Award identifier / Grant number: 2013BJ15

Citation Information: Advances in Nonlinear Analysis, Volume 5, Issue 1, Pages 27–55, ISSN (Online) 2191-950X, ISSN (Print) 2191-9496, DOI: https://doi.org/10.1515/anona-2015-0102.

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