#### Elhoussine Azroul, Abdelmoujib Benkirane, Mohammed Shimi, Mohammed Srati, Three solutions for fractional \$p(x,.)\$-Laplacian Dirichlet problems with weight, Vol. 2020 (2020), Article ID 22, pp. 1-18

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DOI: 10.23952/jnfa.2020.22

Received December 16, 2019; Accepted May 28, 2020; Published June 4, 2020

Abstract. The aim of this paper is to investigate weak solutions for a problem involving the fractional $p(x,.)$-Laplacian operator with weight. The main tool used for obtaining the existence result is a recent three critical-points theorem established by Ricceri. Moreover, we establish some new continuous and compact embedding theorems of the fractional Sobolev spaces with variable exponent into the Hölder spaces.

Elhoussine Azroul, Abdelmoujib Benkirane, Mohammed Shimi, Mohammed Srati, Three solutions for fractional $p(x,.)$-Laplacian Dirichlet problems with weight, Journal of Nonlinear Functional Analysi, Vol. 2020 (2020), Article ID 22, pp. 1-18.