Multiplicity of Solutions for Dirichlet Problem of a Superlinear Fractional p-Laplacian Equation

Authors

  • Tao Zhang Department of Lanzhou Technology and Business College, Lanzhou, Gansu 730101, People’s Republic of China Author
  • WeiQiang Zhang School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People’s Republic of China Author
  • Peihao Zhao School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People’s Republic of China Author

DOI:

https://doi.org/10.47363/JMCA/2022(1)108

Keywords:

Fractional p-Laplacian, Superlinear Reaction, Dirichlet Boundary, Variational Methods, Morse Theory

Abstract

This paper is dedicated to studying the following fractional p-Laplacian problem where Ω⊂ℝN (N ≥ 2) is a bounded domain with C 1,1 boundary, s∈(0,1), 2 ≤ p<N/s, (-Δ) sp is the fractional p-Laplacian and f is a (p-1) superlinearCarathéodory reaction but does not satisfy the usual Ambrosetti-Rabinowitz condition. By using variational methods and Morse theory, we show that the equation has at least three nontrivial solutions: among one of them is positive and one is negative.

Author Biographies

  • Tao Zhang, Department of Lanzhou Technology and Business College, Lanzhou, Gansu 730101, People’s Republic of China

    Department of Lanzhou Technology and Business College, Lanzhou, Gansu 730101, People’s Republic of China 

  • WeiQiang Zhang, School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People’s Republic of China

    School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People’s Republic of China 

  • Peihao Zhao, School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People’s Republic of China

    School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People’s Republic of China 

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Published

2022-11-30

Issue

Vol. 1 No. 4 (2022): Volume 1 Issue 4

Section

Articles