Geodesic
On Scrödinger equation with non-local potential
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, no. 3 (2002), pp. 99-114 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the Schrödinger operator of the form $H=-d^2/dx^2+V$ acting in $L^2({\mathbf R})$ where $V=\varepsilon W(x)+\lambda(\cdot,\phi _0)\phi_0$ is non-local potential. It is proved, that the unique level (i. e. eigenvalue or resonance of the operator $H$) exists for $V=\lambda(\cdot,\phi_0)\phi_0$ for all sufficiently small $\lambda$. We investigate the asymptotic behaviour of level for a small $\lambda$. We prove that there are no levels for $V=\varepsilon W(x)+\lambda(\cdot,\phi_0)\phi_0$ for all sufficiently small $\varepsilon$, if $\lambda \not=0$. 
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     author = {M. S. Smetanina},
     title = {On {Scr\"odinger} equation with non-local potential},
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     pages = {99--114},
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M. S. Smetanina. On Scrödinger equation with non-local potential. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, no. 3 (2002), pp. 99-114. http://geodesic.mathdoc.fr/item/IIMI_2002_3_a1/

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