Journal
MATHEMATISCHE ZEITSCHRIFT
Volume 248, Issue 2, Pages 423-443Publisher
SPRINGER
DOI: 10.1007/s00209-004-0663-y
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We consider the Choquard-Pekar equation -Deltau+Vu=(W*u(2))u uis an element ofH(1) (R-3) and focus on the case of periodic potential V. For a large class of even functions W we show existence and multiplicity of solutions. Essentially the conditions are that 0 is not in the spectrum of the linear part -Delta+V and that W does not change sign. Our results carry over to more general nonlinear terms in arbitrary space dimension Ngreater than or equal to2.
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