Geodesic
A Sturm–Liouville problem with spectral and large parameters in boundary conditions and the associated Cauchy problem
Jamel Ben Amara 1
1 Département de Mathématiques Faculté des Sciences de Tunis Université de Tunis El Manar Tunis, Tunisia
Colloquium Mathematicum, Tome 123 (2011) no. 2, pp. 181-195 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $\varPi _1$. 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.
DOI : 10.4064/cm123-2-2
Keywords: study sturm liouville problem containing spectral parameter boundary conditions associate problem self adjoint operator pontryagin space varpi using operator theoretic formulation analytic methods study asymptotic behavior eigenvalues under variation large physical parameter boundary conditions spectral analysis applied investigate well posedness stability wave equation string

Jamel Ben Amara  1

1 Département de Mathématiques Faculté des Sciences de Tunis Université de Tunis El Manar Tunis, Tunisia 
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Jamel Ben Amara. A Sturm–Liouville problem with spectral
 and large parameters in boundary conditions
 and the associated Cauchy problem. Colloquium Mathematicum, Tome 123 (2011) no. 2, pp. 181-195. doi: 10.4064/cm123-2-2

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