论文标题
对双曲线空间上较高和分数半线性方程的解决方案的对称性
Symmetry of solutions to higher and fractional order semilinear equations on hyperbolic spaces
论文作者
论文摘要
我们表明，具有某些非线性的高级和分数方程的非平凡解决方案是径向对称的，并且在双曲线空间$ \ mathbb {h}^n $中以及整个空间$ \ mathbb {h Mathbb {h}^n $上的地理球上的地质球对非平地。在$ \ mathbb {h}^n $上应用Helgason-fourier分析技术，我们开发了$ \ mathbb {h}^n $上的积分方程的移动平面方法。我们还建立了在欧几里得空间上具有单一术语的某些方程解决方案的对称性。此外，我们获得了涉及分数阶导数的某些半线性方程的解。
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.
