Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2002 · 45 citations · 0 references
Spectral TheoryLagrange Multiplier RuleEngineeringRiemann-hilbert ProblemNonlinear Eigenvalue ProblemEigenvalue ProblemArbitrary Orliczsobolev SpaceGlobal AnalysisFunctional AnalysisNonlinear Functional Analysis
We consider the eigenvalue problem in an arbitrary OrliczSobolev space. We show that the existence of an eigenvalue can be derived from a generalized version of Lagrange multiplier rule. Our approach also applies to more general problems. We emphasize that no 2 condition is imposed.