Resumen de Estimates of the solutions of some asymmetric problem defined on Rn, N ≥ 3

Jacqueline Fleckinger-Pellé

• We study here the following equations defined on IRn, N ≥ 3 (Ef ) (−
  + q(x))u = μm(x)u + f , lim |x|→+∞ u(x) = 0, (Qf ) (−
  + q(x))u = m(x)(au+ − bu−) + f , lim |x|→+∞ u(x) = 0.

  We consider an “intermediate” case where q ≥ 0 grows less than |x|2 and m decreases less than |x|−2 which are the cases usually studied. We study in particular the sign of the solutions for the parameters μ, a, b varying around the associated principal eigenvalue μ∗ defined by (−
  + q(x))u = μ∗m(x)u.