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arXiv · 2210.02278

Symmetry of solutions to higher and fractional order semilinear equations on hyperbolic spaces

Jungang Li·Guozhen Lu·Jianxiong Wang
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Abstract

We show that nontrivial solutions to higher and fractional order equations with certain nonlinearity are radially symmetric and nonincreasing on geodesic balls in the hyperbolic space $\mathbb{H}^n$ as well as on the entire space $\mathbb{H}^n$. Applying the Helgason-Fourier analysis techniques on $\mathbb{H}^n$, we develop a moving plane approach for integral equations on $\mathbb{H}^n$. We also establish the symmetry to solutions of certain equations with singular terms on Euclidean spaces. Moreover, we obtain symmetry to solutions of some semilinear equations involving fractional order derivatives.

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Jungang Li, Guozhen Lu, Jianxiong Wang. 2022-10-05. Symmetry of solutions to higher and fractional order semilinear equations on hyperbolic spaces. https://arxiv.org/abs/2210.02278

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