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Usted está aquí: Inicio / Actividades / Seminarios / Seminario de Ecuaciones Diferenciales No Lineales (SEDNOL) / Actividades del Seminario de Ecuaciones Diferenciales No Lineales / Precise exponential decay for solutions of semilinear elliptic equations and its effect on the structure of the solution set for a real analytic nonlinearity

Precise exponential decay for solutions of semilinear elliptic equations and its effect on the structure of the solution set for a real analytic nonlinearity

Ponente: Nils Ackermann
Institución: IM-UNAM
Tipo de Evento: Investigación
Cuándo 27/08/2015
de 11:00 a 12:00
Dónde Salón de seminarios 3
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  We are concerned with the properties of weak solutions of the
  stationary Schrödinger equation \(-\Delta u + Vu = f(u)\), \(u\in
  H^1(\mathbb{R}^N)\cap L^\infty(\mathbb{R}^N)\), where \(V\) is Hölder
  continuous and \(\inf V>0\).  Assuming \(f\) to be continuous and
  bounded near \(0\) by a power function with exponent larger than \(1\)
  we provide precise decay estimates at infinity for solutions in
  terms of Green's function of the Schrödinger operator.  In some
  cases this improves known theorems on the decay of solutions.  If
  \(f\) is also real analytic on \((0,\infty)\) we obtain that the set of
  positive solutions is locally path connected.  For a periodic
  potential \(V\) this implies that the standard variational functional
  has discrete critical values in the low energy range and that a
  compact isolated set of positive solutions exists, under additional
  assumptions.