论文标题
从其零的非线性schrödinger方程的解决方案的唯一性
Uniqueness of solutions to nonlinear Schrödinger equations from their zeros
论文作者
论文摘要
我们在非线性情况下或存在复杂值的潜力中显示了Schrödinger方程的新型唯一性和刚性结果。作为我们的主要结果，我们可以获得琐碎的解决方案$ u = 0 $是唯一的解决方案$ u（t = 0）\ vert_ {d} = 0，u（t = t）\ vert_ {d} = 0 $ hold，其中$ d \ subset \ subset \ subset \ subset \ subset \ mathbb {r}^d $是某些CodiMesirsirsemensie Onesimensive One的子集。特别是，$ d $对于尺寸$ d = 1 $是离散的。 我们的主要定理可以看作是一个非线性的类似物，这些类似于离散的傅立叶唯一性对，例如著名的radchenko-viazovska公式，以及第二作者的独特性结果和整数力量的苏萨。作为附加应用，我们从其零的某些半线性椭圆方程中推断出刚性结果。
We show novel types of uniqueness and rigidity results for Schrödinger equations in either the nonlinear case or in the presence of a complex-valued potential. As our main result we obtain that the trivial solution $u=0$ is the only solution for which the assumptions $u(t=0)\vert_{D}=0, u(t=T)\vert_{D}=0$ hold, where $D\subset \mathbb{R}^d$ are certain subsets of codimension one. In particular, $D$ is discrete for dimension $d=1$. Our main theorem can be seen as a nonlinear analogue of discrete Fourier uniqueness pairs such as the celebrated Radchenko--Viazovska formula, and the uniqueness result of the second author and M. Sousa for powers of integers. As an additional application, we deduce rigidity results for solutions to some semilinear elliptic equations from their zeros.
