Positive solutions for a coupled systems involving the fractional p(x)- Laplacian operator in unbounded domains

In this paper, we study the existence of at least one weak solution for a class of nonlocal elliptic systems involving the fractional p(x)-Laplacian. These operators are utilized to solve a system defined within unbounded domain. The right sides of systems treated are closely related to a type of gradient C1-functional which satisfy a sublinear growth conditions. Under some additional assumptions on the nonlinearities and leveraging the theory of Lebesgue and fractional Sobolev spaces with variable exponents, we can use a variational approach to establish the existence result.