@article{Kohaupt_2024, title={An Engineering Boundary Eigenvalue Problem Studied by Functional-Analytic Methods}, volume={23}, url={https://www.rajpub.com/index.php/jam/article/view/9574}, DOI={10.24297/jam.v23i.9574}, abstractNote={<p>In this paper, we take up a boundary value problem (BVP) from the area of engineering that is described in a book by L. Collatz. Whereas there, the BVP is cast into a boundary eigenvalue problem (BEVP) having complex eigenvalues, here the original BVP is transformed into a BEVP that has positive simple eigenvalues and real eigenfunctions. Further, unlike there, we derive the inverse T = G of the differential operator L associated with the BEVP, show that T = G is compact in an appropriate real Hilbert space H, expand T u = Gu and u for all u ∈ H in a respective series of eigenvectors, and obtain max-, min-, min-max, and max-min-Rayleigh-quotient representation formulas of the eigenvalues. Specific examples for generalized Rayleigh quotients illustrate the theoretical findings. The style of the paper is expository in order to address a large readership.</p>}, journal={JOURNAL OF ADVANCES IN MATHEMATICS}, author={Kohaupt, L.}, year={2024}, month={Jan.}, pages={11–38} }