| Abstract: |
| In this talk, I will report some recent uniqueness results for the radial solutions to linear and nonlinear Schr\{o}dinger equations involving mixed Laplacian and fractional Laplacian. We prove that the linear equation admits at most one bounded radial solution, provided that the potential is radial, nondecreasing and H\{o}lder continuous. Moreover, the nonlinear Schr\{o}dinger equation possesses a unique ground state solution and is nondegenerate when $s$ is close to $0$ or $1$. |
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