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

2022/10/05 by Jungang Li, Guozhen Lu, Li, Jungang +3
Mathematics · #Nonlinear Differential Equations Analysis #Advanced Differential Equations and Dynamical Systems #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.2210.02278

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 ℍⁿ as well as on the entire space ℍⁿ. Applying the Helgason-Fourier analysis techniques on ℍⁿ, we develop a moving plane approach for integral equations on ℍⁿ. 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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