TY - JOUR
AU - Kohaupt, L.
PY - 2024/01/29
Y2 - 2024/06/19
TI - An Engineering Boundary Eigenvalue Problem Studied by Functional-Analytic Methods
JF - JOURNAL OF ADVANCES IN MATHEMATICS
JA - JAM
VL - 23
IS -
SE - Articles
DO - 10.24297/jam.v23i.9574
UR - https://www.rajpub.com/index.php/jam/article/view/9574
SP - 11-38
AB - <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>
ER -