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

• Autores: Jacqueline Fleckinger-Pellé
• Localización: Monografías de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza, ISSN 1132-6360, Nº. 38, 2012 (Ejemplar dedicado a: Monique Madaune-Tort), págs. 53-64
• Idioma: inglés
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• Resumen

  • 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.