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Fractional Kirchhoff-type problems with exponential growth without the Ambrosetti–Rabinowitz condition

  • Ruichang Pei ORCID logo EMAIL logo
Published/Copyright: February 17, 2021

Abstract

The main aim of this paper is to investigate the existence of nontrivial solutions for a class of fractional Kirchhoff-type problems with right-hand side nonlinearity which is subcritical or critical exponential growth (subcritical polynomial growth) at infinity. However, it need not satisfy the Ambrosetti–Rabinowitz (AR) condition. Some existence results of nontrivial solutions are established via Mountain Pass Theorem combined with the fractional Moser–Trudinger inequality.

MSC 2010: 35A15; 35J60; 35R11

Corresponding author: Ruichang Pei, Department of Mathematics, Tianshui Normal University, Tianshui,741001, P.R. China, E-mail:

Award Identifier / Grant number: 11571176, 11661070, 11764035

Acknowledgements

The author would like to thank the referees for valuable comments and suggestions on improving this paper.

  1. Author contribution: The author read and approved the final manuscript.

  2. Research funding: This research is supported by the NSFC (Nos. 11661070, 11764035 and 11571176) and the Science Foundation of Education Department of Gansu (No. 2018B-48).

  3. Conflict of interest statement: The author declares that he has no competing interest

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Received: 2019-06-18
Revised: 2020-11-20
Accepted: 2021-01-14
Published Online: 2021-02-17
Published in Print: 2022-02-23

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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