A Variational Approach to Superlinear Elliptic Problems

Djairo G. de Figueiredo and Sergio Solimini
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Djairo G. de Figueiredo: Universidade de Brasilia, Departamento de Matematica
Sergio Solimini: Scuola Internazionale Superiore di Studi Avanzati

A chapter in Djairo G. de Figueiredo - Selected Papers, 1984, pp 169-187 from Springer

Abstract: 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.

Date: 1984
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DOI: 10.1007/978-3-319-02856-9_13

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