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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.
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 -