Bulletin of the
Korean Mathematical Society
BKMS
Article
ALL ARTICLES
View
Bull. Korean Math. Soc. 2015; 52(4): 1225-1240
Printed July 31, 2015
https://doi.org/10.4134/BKMS.2015.52.4.1225
Copyright © The Korean Mathematical Society.
On positiveness and contractiveness of the integral operator arising from the beam deflection problem on elastic foundation
Sung Woo Choi
Duksung Women's University
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
Article Tools
Stats or Metrics
Share this article on :
Related articles in BKMS
-
Spectral analysis for the class of integral operators arising from well-posed boundary value problems of finite beam deflection on elastic foundation: characteristic equation
2021; 58(1): 71-111
-
Geometric inequalities for affine connections on Riemannian manifolds
2024; 61(2): 433-450
-
Weighted integral inequalities for modified integral Hardy operators
2022; 59(3): 757-780
-
On the location of eigenvalues of real constant row-sum matrices
2018; 55(6): 1691-1701
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd