A Variational approach to superlinear elliptic problems
- 1 January 1984
- journal article
- research article
- Published by Taylor & Francis in Communications in Partial Differential Equations
- Vol. 9 (7) , 699-717
- https://doi.org/10.1080/03605308408820345
Abstract
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.Keywords
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