Existence and multiplicity results for semilinear equations with measure data

ALBERTO FERRERO, C. SACCON

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Abstract

In this paper, we study existence and nonexistence of solutions for the Dirichlet problem associated with the equation -\Delta u = g(x, u) + \mu where \mu is a Radon measure. Existence and nonexistence of solutions strictly depend on the nonlinearity g(x, u) and suitable growth restrictions are assumed on it. Our proofs are obtained by standard arguments front critical theory and in order to find solutions of the equation, suitable functionals are introduced by mean of approximation arguments and iterative schemes.
Lingua originaleInglese
pagine (da-a)285-318
Numero di pagine34
RivistaTopological Methods in Nonlinear Analysis
Volume28
Numero di pubblicazione2
Stato di pubblicazionePubblicato - 1 gen 2006

Keywords

  • Dirichlet problem
  • Radon measures
  • critical point theory.

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