Abstract
L et be a smooth bounded domain in R N. We consider the semilinear elliptic boundary value problem.
(Received 15 June 1983; received for publication 8 September 1983).
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References
Ambrosetti A. & Prodi G., On the inversion of some differentiable mappings with singularities between Banach spaces,Annali. Math, pura appl. Ser. TV, 93, 231-247 (1972).
Berger M. S. & Podolak E, On the solutions of a nonlinear Dirichlet problem, Indiana Univ. Math. J. 24, 837-846 (1975).
Amann H. & Hess P., A multiplicity result for a class of elliptic boundary value problems, Proc. R. Soc. Edinb. 84 A, 145-151 (1979).
FuĆik S., Remarks on a result by A. Ambrosetti and G. Prodi, Boll. Un. mat. Ital. 11, 259-267 (1975).
Kazdan J. L. & Warner F. W., Remarks on some quasilinear elliptic equations, Communs pure appl. Math. XXVIII, 567-597 (1975).
Dancer E. N., On the ranges of certain weakly nonlinear elliptic partial differential equations, J. Math, pures appl. 57, 351-366 (1978).
Brézis H. & Turner R. L., On a class of superlinear elliptic problems, Communs P.D.E. 2, 601-614 (1977).
Ambrosetti A. & Rabinowitz P., Dual variational methods in critical point theory and applications, J. funct. Analysis 14, 349-381 (1973).
de Figueiredo, D. G., Lectures on boundary value problems of the Ambrosetti-Prodi type, A tas do 12° Seminário Brasileiro de Análise, Sāo Paulo (October 1980).
DE Figueiredo D. G., Lions P. -L. & Nussbaum R., A priori estimates and existence of positive solutions of semilinear elliptic equations, J. Math, pures appl. 61, 41-63 (1982).
Brézis H. & Kato T, Remarks on the Schrödinger operator with singular complex potentials, J. Math, pures appl. 58, 137-151 (1979).
A mann H., On the existence of positive solutions of nonlinear elliptic boundary value problems, Indiana Univ. Math. J. 21, 125-146 (1971).
Sattinger D. H., Topics in Stability and Bifurcation Theory, Springer Lecture Notes in Mathematics, Vol. 309 (1973).
Lazer A. C. & McKenna P. J., On the number of solutions of a nonlinear Dirichlet problem, to appear.
Solimini S, Differential problems with symmetries: equations with jumping nonlinearities, to appear.
Ambrosetti A, Elliptic equtions with jumping nonlinearities, to appear.
Berestycki H. & Lions P. L., Sharp existence results for a class of semilinear elliptic problems, Bol. Soc. Bras. Mat. 12, 9-20 (1981).
Acknowledgments
The author thanks Professor Antonio Ambrosetti for his hospitality at the Scuola Internazionale Superiore di Studi Avanzati (Trieste Italia), where part of this work was done.
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de Figueiredo, D.G. (1984). On The Superlinear Ambrosetti–Prodi Problem. In: Costa, D. (eds) Djairo G. de Figueiredo - Selected Papers. Springer, Cham. https://doi.org/10.1007/978-3-319-02856-9_12
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DOI: https://doi.org/10.1007/978-3-319-02856-9_12
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