We study nonlinear nonlocal problems involving the fractional $p$-Laplacian operator and nonlinearities with negative exponents in the whole space or in an unbounded epigraph domain. The symmetry and monotonicity results are proved by using a direct method of moving planes.

中文翻译：

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无界域中具有负指数的非局部问题的正解的性质

我们研究涉及分数的非线性非局部问题 $p$-Laplacian算子和非线性，在整个空间或在无穷的题词域中具有负指数。通过直接移动平面方法证明了对称性和单调性结果。