scholarly journals On a Sturm-Liouville type problem with retarded argument

2012 ◽  
Vol 36 (1) ◽  
pp. 39-48 ◽  
Author(s):  
Azad Bayramov ◽  
Erdoğan Şen
Keyword(s):  
Retarded Argument ◽  
Type Problem ◽  
Liouville Type ◽  
Sturm Liouville

On a Discontinuous Sturm—Liouville Type Problem with Retarded Argument

2011 ◽  
Author(s):  
Erdoğan Şen ◽  
Azad Bayramov ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras ◽  
...  
Keyword(s):  
Retarded Argument ◽  
Type Problem ◽  
Liouville Type ◽  
Sturm Liouville

Spectrum and Green’s Function of a Many-Interval Sturm–Liouville Problem

2015 ◽  
Vol 70 (5) ◽  
pp. 301-308 ◽  
Author(s):  
Kadriye Aydemir ◽  
Oktay Sh. Mukhtarov
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Resolvent Operator ◽  
Function Method ◽  
Point Spectrum ◽  
Adjoint Operator ◽  
Liouville Problem ◽  
Type Problem ◽  
Liouville Type ◽  
Sturm Liouville

AbstractThis article considers a Sturm–Liouville-type problem on a finite number disjoint intervals together with transmission conditions at the points of interaction. We introduce a new operator-theoretic formulation in such a way that the problem under consideration can be interpreted as a spectral problem for a suitable self-adjoint operator. We investigate some principal properties of eigenvalues, eigenfunctions, and resolvent operator. Particularly, by applying Green’s function method, it is shown that the problem has only point spectrum, and the set of eigenfunctions form a basis of the adequate Hilbert space.

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