Stationary solutions for the non-linear Hartree equation with a slowly varying potential

  • Marta Macrì
  • Margherita Nolasco


We consider the non-linear Hartree equation with a slowly varying external potential \({V_{\varepsilon}}\) and a short range, attractive two-body interaction W. We prove the existence of stationary solutions which are approximatively given by a superposition of several Hartree solitons with their center of mass positions behaving, at the leading order, as classical particles at rest in the background potential \({V_{\varepsilon}}\) .

Mathematics Subject Classification (2000)

35Q55 (35J10) 


Elliptic equation Shadowing lemma 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Dipartimento di Matematica Pura ed ApplicataUniversità di L’AquilaL’AquilaItaly

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