Methods and Applications of Analysis · 2009 · 32 citations · 8 references
Natural SciencesMathematicsPhysicsDifferential EquationsDynamical SystemsTheoretical PhysicsBoundary ConditionsBoundary-value ProblemsEigenvalue ProblemsOperator TheorySpectral AnalysisSpectral TheoryPoint SpectrumSelf-adjoint Eigenvalue ProblemsSelf-adjoint OperatorsSturm - Liouville TheorySturm-liouville TheoryTransmission Conditions
In this paper, we investigate a class of Sturm-Liouville problems with eigenparameter-dependent\nboundary conditions and transmission conditions at an interior point. A self-adjoint linear\noperator $A$ is defined in a suitable Hilbert space $H $such that the eigenvalues of such a problem\ncoincide with those of $A$. We show that the operator $A$ has only point spectrum, the eigenvalues of\nthe problem are algebraically simple, and the eigenfunctions of $A$ are complete in $H$.
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