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Nonlinear boundary value problems at resonance. (English) Zbl 0676.35023
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 N and where the nonlinearity lies between two consecutive eigenvalues.” The type of problem under consideration is Lu=r N u+g(·,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.
Reviewer: B.Kawohl
MSC:
35J65Nonlinear boundary value problems for linear elliptic equations
35J45Systems of elliptic equations, general (MSC2000)
35A05General existence and uniqueness theorems (PDE) (MSC2000)
35B45A priori estimates for solutions of PDE