Multiplicity results for a family of semilinear elliptic problems under local superlinearity and sublinearity
Djairo Guedes de Figueiredo
IMECC - UNICAMP, Campinas, BrazilJean-Pierre Gossez
Université Libre de Bruxelles, BelgiumPedro Ubilla
Universidad de Santiago de Chile, Chile
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Abstract
In this paper we study the existence, nonexistence and multiplicity of positive solutions for the family of problems , , where is a bounded domain in , and is a parameter. The results include the well-known nonlinearities of the Ambrosetti–Brezis–Cerami type in a more general form, namely , where . The coefficient is assumed nonnegative but is allowed to change sign, even in the critical case. The notions of local superlinearity and local sublinearity introduced in [9] are essential in this more general framework. The techniques used in the proofs are lower and upper solutions and variational methods.
Cite this article
Djairo Guedes de Figueiredo, Jean-Pierre Gossez, Pedro Ubilla, Multiplicity results for a family of semilinear elliptic problems under local superlinearity and sublinearity. J. Eur. Math. Soc. 8 (2006), no. 2, pp. 269–288
DOI 10.4171/JEMS/52