Existence of infinitely many solutions for a nonlocal problem

Jing Yang; Jing Yang

doi:10.3934/math.2020369

AIMS Mathematics

2020, Volume 5, Issue 6: 5743-5767. doi: 10.3934/math.2020369

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Research article

Existence of infinitely many solutions for a nonlocal problem

Jing Yang ^,

School of science, Jiangsu University of Science and Technology, Zhenjiang 212003, P. R. China

Received: 12 May 2020 Accepted: 22 June 2020 Published: 10 July 2020
MSC : 35B33, 35J60

In this paper, we deal with a class of fractional Hénon equation and by using the Lyapunov-Schmidt reduction method, under some suitable assumptions, we derive the existence of infinitely many solutions, whose energy can be made arbitrarily large. Compared to the previous works, we encounter some new challenges because of the nonlocal property for fractional Laplacian. But by doing some delicate estimates for the nonlocal term we overcome the difficulty and find infinitely many nonradial solutions.
- fractional Laplacian,
- critical exponent,
- reduction method
Citation: Jing Yang. Existence of infinitely many solutions for a nonlocal problem[J]. AIMS Mathematics, 2020, 5(6): 5743-5767. doi: 10.3934/math.2020369

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Abstract

In this paper, we deal with a class of fractional Hénon equation and by using the Lyapunov-Schmidt reduction method, under some suitable assumptions, we derive the existence of infinitely many solutions, whose energy can be made arbitrarily large. Compared to the previous works, we encounter some new challenges because of the nonlocal property for fractional Laplacian. But by doing some delicate estimates for the nonlocal term we overcome the difficulty and find infinitely many nonradial solutions.

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