论文标题
伪宗教施罗丁运营商的直接方法
Direct methods for pseudo-relativistic Schrödinger operators
论文作者
论文摘要
在本文中，我们建立了各种最大原理，并开发了涉及物理有趣（非局部）伪偏移的方程式的直接移动平面和滑动方法。结果，我们还得出了这些直接方法的多个应用。例如，我们证明了涉及操作员$（δ+m^{2}}）$（ - δ+m^{2}）^{s} $的各个方程式的单调性，对称性和独特性结果非线性。
In this paper, we establish various maximal principles and develop the direct moving planes and sliding methods for equations involving the physically interesting (nonlocal) pseudo-relativistic Schrödinger operators $(-Δ+m^{2})^{s}$ with $s\in(0,1)$ and mass $m>0$. As a consequence, we also derive multiple applications of these direct methods. For instance, we prove monotonicity, symmetry and uniqueness results for solutions to various equations involving the operators $(-Δ+m^{2})^{s}$ in bounded domains, epigraph or $\mathbb{R}^{N}$, including pseudo-relativistic Schrödinger equations, 3D boson star equations and the equations with De Giorgi type nonlinearities.
