Abstract.
We consider the Choquard-Pekar equation 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 −Δ+V and that W does not change sign. Our results carry over to more general nonlinear terms in arbitrary space dimension N≥2.
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Mathematics Subject Classification (2000):35Q55, 35Q40, 35J10, 35J20, 35J60, 46N50, 49J35, 81V70
in final form: 14 November 2003
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Ackermann, N. On a periodic Schrödinger equation with nonlocal superlinear part. Math. Z. 248, 423–443 (2004). https://doi.org/10.1007/s00209-004-0663-y
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DOI: https://doi.org/10.1007/s00209-004-0663-y