×

Double resonance and multiple solutions for semilinear elliptic equations. (English) Zbl 0575.35032

Second order semilinear equations on a bounded domain are considered for nonlinearities that at infinity give double resonance. The author shows some multiplicity results for Ambrosetti-Mancini type as in the case of non-resonating problems.
Reviewer: J.I.Diaz

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35J25 Boundary value problems for second-order elliptic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
PDFBibTeX XMLCite
Full Text: Numdam EuDML

References:

[1] A. Ambrosetti - G. Mancini , Sharp non uniqueness results for some nonlinear problems , Nonlinear Analysis TMA , Vol. 3 , No. 5 , pp. 635 - 645 . MR 541874 | Zbl 0433.35025 · Zbl 0433.35025 · doi:10.1016/0362-546X(79)90092-0
[2] H. Berestycki - G. DE FIGUEIREDO, Double resonance in semilinear elliptic problems , Comm. in PDE , 6 ( 1 ) ( 1981 ), pp. 91 - 120 . MR 597753 | Zbl 0468.35043 · Zbl 0468.35043 · doi:10.1080/03605308108820172
[3] T. Gallouet - O. Kavian , Résultats d’existence et de non existence de solutions pour certains problèmes demi-linéaires à l’infini , Ann. Sc. de Toulouse ( 1981 ). Numdam | MR 658734 | Zbl 0495.35001 · Zbl 0495.35001 · doi:10.5802/afst.568
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.