Arshyn Altybay, Michael Ruzhansky, Mohammed Elamine Sebih, Niyaz Tokmagambetov
Published 2020-04-21Version 1
In this paper, we consider the space-fractional Schr\"{o}dinger equation with a singular potential. We show that it has a so-called very weak solutions. The uniqueness and consistency results are proved in an appropriate sense. Numerical simulations are done, and a particle accumulating effect is observed. From the mathematical point of view, a "splitting of the strong singularity" phenomena is observed.
Comments: 14 pages; 17 figures
Existence of infinitely many solutions for a class of fractional Schrödinger equations in $\mathbb{R}^N$ with combined nonlinearities
Existence of nonnegative solutions for fractional Schrödinger equations with Neumann condition
Ground state solutions of fractional Schrödinger equations with potentials and weak monotonicity condition on the nonlinear term
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