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Published in:
2013 | OriginalPaper | Chapter
A Variational Approach to Superlinear Elliptic Problems
Authors : Djairo G. de Figueiredo, Sergio Solimini
Published in: Djairo G. de Figueiredo - Selected Papers
Publisher: Springer International Publishing
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This paper contains a variational treatment of the Ambrosetti-Prodi problem, including the superlinear case. The main result extends previous ones by Kazdan-Warner, Amann-Hess, Dancer, K. C. Chang and de Figueiredo. The required abstract results on critical point theory of functionals in Hilbert space are all proved using Ekeland’s variational principle. These results apply as well to other superlinear elliptic problems provided an ordered pair of a sub- and a supersolution is exhibited.