ON GLM TYPE MAIN INTEGRAL EQUATION FOR SINGULAR STURM-LIOUVILLE OPERATOR WHICH HAS DISCONTINUOUS COEFFICIENT


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Topsakal N. , Amirov R. , Ergün A.

EJONS International Congress on Mathematic, Engineering and Natural Sciences-III, Mardin, Türkiye, 21 - 22 Nisan 2018, ss.1-2

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: Mardin
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.1-2

Özet

We consider the boundary value problem L for the equation:

, ,

with the boundary conditions

and with the jump conditions

where λ is spectral parameter; , -is a real valued bounded function

and .

Boundary value problems with discontinuous coefficient often appear in applied mathematics, geophysics,

mechanics, electromagnetics, elasticity and other branches of engineering and physics. The inverse problem

of reconstructing the material properties of a medium from data collected outside of the medium is of central

importance in disciplines ranging from engineering to the geosciences. For example, torodial vibrations and

free vibrations of the earth, reconstructing the discontinuous material properties of a nonabsorbing media, as

a rule leads to direct and inverse problems or the Sturm-Liouville equation which has discontinuous

coefficient. [1-3]

In this study, we derive Gelfand-Levitan-Marchenko type main integral equation of inverse problem for

singular Sturm-Liouville equation which has discontinuous coefficient. Then we prove the unique solvability

of the main integral equation.