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The main objective of this paper is to establish the convergence for thefractional $p$-Laplacian of nonnegative sequence of functions with $p>2$.Further, we show the blow-up phenomena for solutions to the extended Nirenbergproblem modeled by fractional $p$-Laplacian with the prescribed negativefunctions.

Convergence for the fractional $p$-Laplacian and its corresponding extended Nirenberg problem