A Sturm-Liouville problem with spectral and large parameters in boundary conditions and the associated Cauchy problem

Jamel Ben Amara. "A Sturm-Liouville problem with spectral and large parameters in boundary conditions and the associated Cauchy problem." Colloquium Mathematicae 123.2 (2011): 181-195. <http://eudml.org/doc/283594>.

@article{JamelBenAmara2011,
abstract = {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.},
author = {Jamel Ben Amara},
journal = {Colloquium Mathematicae},
keywords = {Sturm-Liouville problem; spectral parameter in boundary conditions; asymptotics of eigenvalues; Pontryagin space},
language = {eng},
number = {2},
pages = {181-195},
title = {A Sturm-Liouville problem with spectral and large parameters in boundary conditions and the associated Cauchy problem},
url = {http://eudml.org/doc/283594},
volume = {123},
year = {2011},
}

TY - JOUR
AU - Jamel Ben Amara
TI - A Sturm-Liouville problem with spectral and large parameters in boundary conditions and the associated Cauchy problem
JO - Colloquium Mathematicae
PY - 2011
VL - 123
IS - 2
SP - 181
EP - 195
AB - 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.
LA - eng
KW - Sturm-Liouville problem; spectral parameter in boundary conditions; asymptotics of eigenvalues; Pontryagin space
UR - http://eudml.org/doc/283594
ER -