Nonexistence Results for the Elliptic Equations with Fractional Laplacian and Variable Exponents Nonlinearities

The main motivation behind this paper is to investigate the nonexistence of weak solution for the following Cauchy problem (-∆) and(-∆) γ 2 is the fractional Laplacian operator of order γ 2 .Then, this result is extended to the case of 2 × 2-system of the same type.The proof of our results is based on a contradiction argument by using the so-called test function method.The results obtained in this paper extend several contributions and we focus on new nonexistence result which is due to the presence of variable-exponents