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EnglishWe consider a parametric nonlinear elliptic equation driven by the Dirichlet p-Laplacian. We study the existence, nonexistence and multiplicity of positive solutions as the parameter varies in the set of positive reals and the potential exhibits a p-superlinear growth, without satisfying the usual in such cases Ambrosetti–Rabinowitz condition. We prove a bifurcation-type result when the reaction has (p-1)-sublinear terms near zero (problem with concave and convex nonlinearities). We show that a similar bifurcation-type result is also true, if near zero the right hand side is (p-1)-linear.
Existence, nonexistence and multiplicity of positive solutions for parametric nonlinear elliptic equations / IANNIZZOTTO A; PAPAGEORGIOU N. - 51:1(2014), pp. 179-202.
| Titolo: | Existence, nonexistence and multiplicity of positive solutions for parametric nonlinear elliptic equations |
| Autori: | |
| Data di pubblicazione: | 2014 |
| Rivista: | |
| Citazione: | Existence, nonexistence and multiplicity of positive solutions for parametric nonlinear elliptic equations / IANNIZZOTTO A; PAPAGEORGIOU N. - 51:1(2014), pp. 179-202. |
| Abstract: | We consider a parametric nonlinear elliptic equation driven by the Dirichlet p-Laplacian. We study the existence, nonexistence and multiplicity of positive solutions as the parameter varies in the set of positive reals and the potential exhibits a p-superlinear growth, without satisfying the usual in such cases Ambrosetti–Rabinowitz condition. We prove a bifurcation-type result when the reaction has (p-1)-sublinear terms near zero (problem with concave and convex nonlinearities). We show that a similar bifurcation-type result is also true, if near zero the right hand side is (p-1)-linear. |
| Handle: | http://hdl.handle.net/11584/48798 |
| Tipologia: | 1.1 Articolo in rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| Iannizzotto-Papageorgiou-OJM.pdf | Articolo principale | versione editoriale | Open Access Visualizza/Apri |
http://hdl.handle.net/11584/48798
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