Geodesic
On the existence of a~countable set of solutions in a problem of polaron theory
Sbornik. Mathematics, Tome 75 (1993) no. 1, pp. 247-255

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An investigation is made of a certain nonlinear second-order integro-differential equation having numerous applications in various areas of physics (polaron theory, the theory of many-particle quantum systems, and so on). Under certain assumptions it is proved that there is a positive solution, and, moreover, an infinite set of distinct solutions. Use is made of the Lyusternik–Shnirel'man theory of critical points and the fibering method of S. I. Pokhozhaev. 
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     title = {On the existence of a~countable set of solutions in a problem of polaron theory},
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P. E. Zhidkov. On the existence of a~countable set of solutions in a problem of polaron theory. Sbornik. Mathematics, Tome 75 (1993) no. 1, pp. 247-255. http://geodesic.mathdoc.fr/item/SM_1993_75_1_a13/