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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 11
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Research Article

Existence and multiplicity of solutions for perturbed fractional p-Laplacian equations with critical nonlinearity in N

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Pages 2960-2977 | Received 02 Nov 2021, Accepted 10 Feb 2022, Published online: 03 Mar 2022
 

Abstract

In this paper, we consider the existence and multiplicity of solutions for the following perturbed fractional p-Laplacian equation {ϵsp(Δ)psu+V(x)|u|p2u=A(x)|u|ps2u+h(x,u),xRN,u(x)0,as|x|. Under some mild conditions on V, A and h, we show that the problem has at least one positive weak solution provided ϵεσ, and for any mN, it has m pairs of solutions if ϵεmσ, where εσ and εmσ are sufficiently small positive numbers. Moreover, these solutions uϵ0 in Ws,p(RN) as ϵ0.

2020 Mathematics Subject Classifications:

Acknowledgments

The authors would like to express sincere thanks to the anonymous referee for his/her carefully reading the manuscript and valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Project Supported by the Anhui Provincial Natural Science Foundation [grant number 1808085QA15]; the Scientific Research Project of Anhui University of Finance and Economics [grant number ACKYC19050] and the Natural Science Foundation of China [grant number 11571093].

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