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Mathematische Zeitschrift

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

On a periodic Schrödinger equation with nonlocal superlinear part

  • Nils Ackermann
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.

Keywords

Large Class Nonlinear Term Linear Part Space Dimension Periodic Potential 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Justus-Liebig-UniversitätMathematisches InstitutGiessenGermany

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