A direct proof of stability of nonnegative weak solution for fractional \(\mathbf{p}\)-Laplacian problem with concave nonlinearity

The present paper provides a direct proof of stability of nontrivial nonnegative weak solution for fractional \(p\)-Laplacian problem under concave nonlinearity condition. The main results of this work are extend the previously known results for the fractional Laplacian problem.