Nonexistence results of solutions for some fractional $p$-Laplacian equations in $\mathbb{R}^{N}$

In the present paper, we study the nonexistence of nontrivial weak solutions to a class of fractional $p$-Laplacian equation in two cases which are $sp > N$ and $sp < N$. In each of these cases, by using fractional Laplacian theory and inequality techniques, we obtain concrete range of parameter for which nontrivial weak solution of the problem does not exist. Our work complements the known nonexistence results in this direction.