We consider a system governed by the fractional Schödinger operator with a delta potential supported by a circle in $\mathbb {R}^2$. We find out the function counting the number of bound states, in particular, we give the necessary and sufficient conditions for the absence of bound state in our system. Furthermore, we reproduce the form of eigenfunctions and analyze the asymptotic behavior of eigenvalues for the strong coupling constant case.
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2012
American Institute of Physics
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