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SETSCI - Volume 3 (2018)
ISAS2018-Winter - 2nd International Symposium on Innovative Approaches in Scientific Studies, Samsun, Turkey, Nov 30, 2018

Coercive Solvability of Many-Interval Sturm-Liouville Problems (ISAS2018-Winter_212)
O. Sh.  Mukhtarov 1*, Kadriye Aydemir2, Hayati Olgar3
1AzerbaijanNational Academy of Sciences , Bakü, Azerbaijan
2Amasya University, Amasya, Turkey
3Tokat Gaziosmanpaşa University, Tokat, Turkey
* Corresponding author: omukhtarov@yahoo.com
Published Date: 2019-01-14   |   Page (s): 1103-1106   |    24     6

ABSTRACT It is well-known that the Sturm-Liouville type boundary value problems appears in solving many important problems in
physics. For example, some problems of theory of elasticity in a half-strip ,the problems of theory of vibrations of an elastic cylinder
reduce to investigation of solvability of appropriate boundary value problems for Sturm-Liouville type differential equations. In the
recent years, the Sturm-Liouville type boundary value problems with additional transmission conditions are investigated by many
mathematical and physical researches . Note that, such type problems is very complicated because boundary value problems with
additional transmission conditions may be not self-adjoint in the classical Hilbert space L2 and therefore the eigenvalues may be
not real.
The main goal of this study is to prove coerciveness of a new class many interval Sturm-Liouville problems with additional
transmission conditions at the points of interaction. Moreover we shall establish some spectral properties and find asymptotic
behaviour of the eigenvalues of the problem under consideration.
Observe that this type of problems is studied in the setting of the direct sum of the Hilbert space. We also construct fundamental solutions and discuss some properties of spectrum. 
KEYWORDS Boundary value problem, transmission conditions, Coercive solvability, spectrum, Hilbert space.
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