SYMMETRY AND MONOTONICITY OF POSITIVE SOLUTIONS TO THE FRACTIONAL $p$-LAPLACIAN EQUATIONS
Keywords:
fractional p-Laplacian, symmetry, monotonicity, singular nonlinearities, positive solutionDOI:
https://doi.org/10.17654/0972096026001Abstract
This paper is devoted to study the fractional $p$-Laplacian equation with singular nonlinearities. We use the direct method of moving planes to derive the symmetry and monotonicity result of positive solutions to the fractional $p$-Laplacian equations with singular nonlinearities. Compared to the work proposed in Hu [13], we extend the results of fractional Laplacian to $p$-Laplacian in a bounded domain. In addition, we also consider a singular nonlinear elliptic equation with fractional $p$-Laplacian term in $\mathrm{P}^n \backslash\{0\}$.
Received: September 7, 2025
Revised: October 1, 2025
Accepted: October 27, 2025
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