Spectral theory of one perturbed boundary value problem with interior singularities

The purpose of this study is to investigate a new class of Sturm-Liouville problems generated by the differential-operator equation −a(x)u"+q(x)u+B1u|x = λu on two disjoint intervals under eigendependent boundary and transmission conditions. By suggesting own approaches we establish an isomorph...

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Bibliographic Details
Main Authors: Mukhtarov Oktay Sh, Aydemir Kadriye, Olğar Hayati
Format: Conference Proceeding
Language:English
Subjects:
Boundary value problems
Coercivity
Differential equations
Eigenvalues
Hilbert space
Isomorphism
Operators (mathematics)
Singularities
Spectral theory
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Summary:The purpose of this study is to investigate a new class of Sturm-Liouville problems generated by the differential-operator equation −a(x)u"+q(x)u+B1u|x = λu on two disjoint intervals under eigendependent boundary and transmission conditions. By suggesting own approaches we establish an isomorphism and coerciveness with respect to spectral parameter and get maximal decreasing of the norm of resolvent operator in suitable Hilbert spaces. Finally, we prove the discreteness of the spectrum and derive asymptotic formulas for the eigenvalues.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.4893848