Research article

Existence of infinitely many solutions for a nonlocal problem

  • 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.

    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

    Related Papers:

  • 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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