Local ‘Superlinearity’ and ‘Sublinearity’ for the p-Laplacian

Djairo G. de Figueiredo (), Jean-Pierre Gossez () and Pedro Ubilla ()
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Djairo G. de Figueiredo: IMECC-UNICAMP
Jean-Pierre Gossez: Université Libre de Bruxelles, Département de Mathématique, C.P. 214
Pedro Ubilla: Universidad de Santiago de Chile

A chapter in Djairo G. de Figueiredo - Selected Papers, 2009, pp 697-728 from Springer

Abstract: Abstract We study the existence, nonexistence and multiplicity of positive solutions for a family of problems $$ - \Updelta_{p} u = f_{\lambda } \,(x,\,u),\,u \in \,W_{0}^{1,p} (\Upomega ) $$ , where Ω is a bounded domain in $$ {\mathbb{R}}^{N} ,\,N > p $$ , and λ > 0 is a parameter. The family we consider includes the well-known nonlinearities of Ambrosetti–Brezis–Cerami type in a more general form, namely $$ \lambda a(x)u^{q} + b(x)u^{r} $$ , where $$ 0 \leqslant q

Keywords: p-Laplacian; Concave-convex nonlinearities; Critical exponent; $$ C_{0}^{1} Z $$ versus $$ W_{0}^{1; p} $$ local minimization; Strong comparison principle; C 1; α estimate; Upper–lower solutions (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-02856-9_43

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DOI: 10.1007/978-3-319-02856-9_43

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