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Zbl 0676.35023
Iannacci, R.; Nkashama, M.N.
Nonlinear boundary value problems at resonance.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 11, 455-473 (1987). ISSN 0362-546X

From the paper: It is the purpose of this paper to present some very general abstract results which unify and generalize most of the known existence theorems for the case when resonance occurs at the eigenvalue $r\sb N$ and where the nonlinearity lies between two consecutive eigenvalues.'' The type of problem under consideration is $Lu=r\sb Nu+g(\cdot,u)=h$ with L being a linear differential operator. The main result is an existence theorem under suitable assumptions. Applications and counterexamples illuminate the scope of the result. Ingredients of the proof are degree arguments and a priori estimates.
[B.Kawohl]
MSC 2000:
*35J65 (Nonlinear) BVP for (non)linear elliptic equations
35J45 Systems of elliptic equations, general
35A05 General existence and uniqueness theorems (PDE)
35B45 A priori estimates

Keywords: Landesman-Lazer condition; abstract results; existence; resonance; eigenvalue; nonlinearity; degree arguments; a priori estimates

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