Mathematische Zeitschrift

, Volume 248, Issue 2, pp 423–443 | Cite as

On a periodic Schrödinger equation with nonlocal superlinear part

Article

Abstract.

We consider the Choquard-Pekar equation Open image in new window 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Justus-Liebig-UniversitätMathematisches InstitutGiessenGermany

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