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On the sign of the solutions to some semilinear Dirichlet problems

Published online by Cambridge University Press:  14 November 2011

Vittorio Cafagna  and
Flavio Donati
Vittorio Cafagna
Affiliation:
Istituto di Matematica, Università dell'Aquila, Via Roma 33, 67100 L'Aquila, Italy
Flavio Donati
Affiliation:
Istituto di Matematica, Università dell'Aquila, Via Roma 33, 67100 L'Aquila, Italy
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Synopsis

We study the sign of solutions to a class of semilinear Dirichlet problems when the nonlinearity is, for instance, a concave-convex function which interacts with the spectrum of the linear part. We are able to prove, in some cases, exact multiplicity results for positive and negative solutions. For the proofs we employ a device which splits the given problem into two others satisfying a suitable version of the Ambrosetti–Prodi result.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 99 , Issue 3-4 , 1985 , pp. 359 - 369
Copyright
Copyright © Royal Society of Edinburgh 1985

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