Geodesic
On Scrödinger equation with non-local potential
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, no. 3 (2002), pp. 99-114 
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/
@article{IIMI_2002_3_a1,
     author = {M. S. Smetanina},
     title = {On {Scr\"odinger} equation with non-local potential},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {99--114},
     year = {2002},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2002_3_a1/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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