We study a Sturm-Liouville problem containing a spectral parameter in the boundary conditions. We associate to this problem a self-adjoint operator in a Pontryagin space Π₁. Using this operator-theoretic formulation and analytic methods, we study the asymptotic behavior of the eigenvalues under the variation of a large physical parameter in the boundary conditions. The spectral analysis is applied to investigate the well-posedness and stability of the wave equation of a string.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm123-2-2,
author = {Jamel Ben Amara},
title = {A Sturm-Liouville problem with spectral and large parameters in boundary conditions and the associated Cauchy problem},
journal = {Colloquium Mathematicae},
volume = {122},
year = {2011},
pages = {181-195},
zbl = {1230.34029},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm123-2-2}
}
Jamel Ben Amara. A Sturm-Liouville problem with spectral and large parameters in boundary conditions and the associated Cauchy problem. Colloquium Mathematicae, Tome 122 (2011) pp. 181-195. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm123-2-2/