On positiveness and contractiveness of the integral operator arising from the beam deflection problem on elastic foundation
Bull. Korean Math. Soc. 2015 Vol. 52, No. 4, 1225-1240
https://doi.org/10.4134/BKMS.2015.52.4.1225
Published online July 31, 2015
Sung Woo Choi
Duksung Women's University
Abstract : We provide a complete proof that there are no eigenvalues of the integral operator $\mathcal{K}_l$ outside the interval $(0,1/k)$. $\mathcal{K}_l$ arises naturally from the deflection problem of a beam with length $2l$ resting horizontally on an elastic foundation with spring constant $k$, while some vertical load is applied to the beam.
Keywords : beam, deflection, elastic foundation, integral operator, eigenvalue, $L^2$-norm
MSC numbers : Primary 34L15, 47G10, 74K10
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