Electronic Journal of Differential Equations, 
Vol. 2021 (2021), No. 16, pp. 1-15.

Title: Infinitely many solutions for a nonlocal type problem with sign-changing weight function
       
Authors: Elhoussine Azroul     (Sidi Mohamed Ben Abdellah Univ., Fez, Morocco)
         Abdelmoujib Benkirane (Sidi Mohamed Ben Abdellah Univ., Fez, Morocco)
         Mohammed Srati        (Sidi Mohamed Ben Abdellah Univ., Fez, Morocco)
         Cesar Torres (Univ. Nacional de Trujillo, Peru)

Abstract:
 In this article, we study the existence of weak solutions for a
 fractional type problem driven by a nonlocal operator of elliptic type
 $$\displaylines{
 (-\Delta)^s_{a_1} u -\lambda a_2(|u|)u = f(x,u)+g(x)|u|^{q(x)-2}u \quad \text{in } \Omega \cr
 u = 0 \quad \text{in } \mathbb{R}^N\setminus \Omega.
 }$$
 Our approach is based on critical point theorems and variational methods.

Submitted June 21, 2020. Published March 18, 2021.
Math Subject Classifications: 35R1, 35P30, 35J20, 58E05.
Key Words: Fractional Orlicz-Sobolev spaces; critical point theorems; variational methods.