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Yıl 2018, Cilt: 10, 121 - 125, 29.12.2018

Öz

Kaynakça

  • Allahverdiev, B. P., Bairamov, E. and E. Ugurlu, Eigenparameter dependent Sturm-Liouville problems in boudary conditions with transmissionconditions, J. Math. Anal. Appl. 401, 88-396 (2013).
  • Akbarfam, I., A. Jodayree A., Resolvent Operator and Self-Adjointness of Sturm-Liouville Operators with a Finite Number of TransmissionConditions, Mediterranean Journal Of Mathematics, 11(2), 447-462(2014).
  • Ao J. and Sun J. Matrix representations of SturmˆuLiouville problems with coupled eigenparameter-dependent boundary conditions, AppliedMathematics and Computation 244, 142ˆu148(2014).
  • Aydemir, K., Mukhtarov, O., A Class of Sturm-Liouville Problems with Eigenparameter Dependent Transmission Conditions, NumericalFunctional Analysis and Optimization, (2017), Doi: 10.1080/01630563.2017.1316995.
  • Aydemir, K., Ol˘gar, H., Mukhtarov, O. Sh. and Muhtarov, F. S., Di erential operator equations with interface conditions in modified directsum spaces, Filomat, 32:3 (2018), 921-931.
  • Bairamov, E. and Ugurlu, E. On the characteristic values of the real component of a dissipative boundary value transmission problem, Appl.Math. and Comp. 218, 9657-9663(2012).
  • Cannon J. R. and Meyer, G.H.On a Di usion in a Fractured Medium, SIAM J. Appl. Math., 3, 434-448(1971).[8] Hıra F.and Altınıs¸ık N., Sampling theorems for Sturm-Liouville problem with moving discontinuity points, Boundary Value Problems,2014:237(2014).
  • Hıra F.and Altınıs¸ık N., Sampling theorems for Sturm-Liouville problem with moving discontinuity points, Boundary Value Problems, 2014:237(2014).
  • Kandemir, M. and Mukhtarov, O. Sh., Nonlocal Sturm-Liouville Problems with Integral Terms in the Boundary Conditions, Electronic Journalof Di erential Equations, Vol. 2017 (2017), No. 11, pp. 1-12.
  • Mukhtarov, O.Sh., Olˇgar, H. and Aydemir, K., Resolvent Operator and Spectrum of New Type Boundary Value Problems, Filomat, 29:7 (2015),1671-1680.
  • Olğar, H. and Mukhtarov, O. Sh.,Weak Eigenfunctions Of Two-Interval Sturm-Liouville Problems TogetherWith Interaction Conditions, Journalof Mathematical Physics, 58, 042201, DOI: 10.1063/1.4979615 (2017).
  • Olğar, H., Mukhtarov, O. Sh. and Aydemir, K., Some properties of eigenvalues and generalized eigenvectors of one boundary value problem, Filomat, 32:3, 911-920(2018).
  • Pham Huy H. and Sanchez-Palencia E., Ph enomenes des transmission a travers des couches minces de conductivite elevee J. Math. Anal.Appl., 47, 284-309(1974).

Comparison Theorems for One Sturm-Liouville Problem with Nonlocal Boundary Conditions

Yıl 2018, Cilt: 10, 121 - 125, 29.12.2018

Öz

n this study we present a new approach for investigation of some
Sturm-Liouville systems with nonlocal boundary conditions. In the
theory of boundary value problems for two-order differential
equations the basic concepts and methods have been formulated
studying the problems of classical mathematical physics. However,
many modern problems, which arise as the mathematical modeling of
some systems and processes in the fields of physics, such as the
vibration of strings, the interaction of atomic particles motivate
to formulate and investigate the new ones, for example, a class of
Sturm-Liouville problems with nonlocal boundary conditions. Such
conditions arise when we cannot measure data directly at the
boundary. In this case, the problem is formulated, where the value
of the solution and its derivative is linked to interior points of
the considered interval. Sturm-Liouville problems together with
transmission conditions at some interior points is very important
for solving many problems of mathematical physics. In this study we
present a new approach for investigation of boundary value problems
consisting of the two interval Sturm-Liouville equations. This kind
of boundary value transmission problems are connected with various
physical transfer problems (for example, heat and mass transfer
problems). We define a new Hilbert space and linear differential
operator in it such a way that the considered nonlocal problem can
be interpreted as an spectral problem.  We investigate the main
spectral properties of the problem under consideration. Particularly
we present a new criteria for Sturm-Comparison theorems. Our main
result generalizes the classical comparison theorem for regular
Sturm-Liouville problems.

Kaynakça

  • Allahverdiev, B. P., Bairamov, E. and E. Ugurlu, Eigenparameter dependent Sturm-Liouville problems in boudary conditions with transmissionconditions, J. Math. Anal. Appl. 401, 88-396 (2013).
  • Akbarfam, I., A. Jodayree A., Resolvent Operator and Self-Adjointness of Sturm-Liouville Operators with a Finite Number of TransmissionConditions, Mediterranean Journal Of Mathematics, 11(2), 447-462(2014).
  • Ao J. and Sun J. Matrix representations of SturmˆuLiouville problems with coupled eigenparameter-dependent boundary conditions, AppliedMathematics and Computation 244, 142ˆu148(2014).
  • Aydemir, K., Mukhtarov, O., A Class of Sturm-Liouville Problems with Eigenparameter Dependent Transmission Conditions, NumericalFunctional Analysis and Optimization, (2017), Doi: 10.1080/01630563.2017.1316995.
  • Aydemir, K., Ol˘gar, H., Mukhtarov, O. Sh. and Muhtarov, F. S., Di erential operator equations with interface conditions in modified directsum spaces, Filomat, 32:3 (2018), 921-931.
  • Bairamov, E. and Ugurlu, E. On the characteristic values of the real component of a dissipative boundary value transmission problem, Appl.Math. and Comp. 218, 9657-9663(2012).
  • Cannon J. R. and Meyer, G.H.On a Di usion in a Fractured Medium, SIAM J. Appl. Math., 3, 434-448(1971).[8] Hıra F.and Altınıs¸ık N., Sampling theorems for Sturm-Liouville problem with moving discontinuity points, Boundary Value Problems,2014:237(2014).
  • Hıra F.and Altınıs¸ık N., Sampling theorems for Sturm-Liouville problem with moving discontinuity points, Boundary Value Problems, 2014:237(2014).
  • Kandemir, M. and Mukhtarov, O. Sh., Nonlocal Sturm-Liouville Problems with Integral Terms in the Boundary Conditions, Electronic Journalof Di erential Equations, Vol. 2017 (2017), No. 11, pp. 1-12.
  • Mukhtarov, O.Sh., Olˇgar, H. and Aydemir, K., Resolvent Operator and Spectrum of New Type Boundary Value Problems, Filomat, 29:7 (2015),1671-1680.
  • Olğar, H. and Mukhtarov, O. Sh.,Weak Eigenfunctions Of Two-Interval Sturm-Liouville Problems TogetherWith Interaction Conditions, Journalof Mathematical Physics, 58, 042201, DOI: 10.1063/1.4979615 (2017).
  • Olğar, H., Mukhtarov, O. Sh. and Aydemir, K., Some properties of eigenvalues and generalized eigenvectors of one boundary value problem, Filomat, 32:3, 911-920(2018).
  • Pham Huy H. and Sanchez-Palencia E., Ph enomenes des transmission a travers des couches minces de conductivite elevee J. Math. Anal.Appl., 47, 284-309(1974).
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Kadriye Aydemir

Hayati Olğar

Oktay Mukhtarov

Yayımlanma Tarihi 29 Aralık 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 10

Kaynak Göster

APA Aydemir, K., Olğar, H., & Mukhtarov, O. (2018). Comparison Theorems for One Sturm-Liouville Problem with Nonlocal Boundary Conditions. Turkish Journal of Mathematics and Computer Science, 10, 121-125.
AMA Aydemir K, Olğar H, Mukhtarov O. Comparison Theorems for One Sturm-Liouville Problem with Nonlocal Boundary Conditions. TJMCS. Aralık 2018;10:121-125.
Chicago Aydemir, Kadriye, Hayati Olğar, ve Oktay Mukhtarov. “Comparison Theorems for One Sturm-Liouville Problem With Nonlocal Boundary Conditions”. Turkish Journal of Mathematics and Computer Science 10, Aralık (Aralık 2018): 121-25.
EndNote Aydemir K, Olğar H, Mukhtarov O (01 Aralık 2018) Comparison Theorems for One Sturm-Liouville Problem with Nonlocal Boundary Conditions. Turkish Journal of Mathematics and Computer Science 10 121–125.
IEEE K. Aydemir, H. Olğar, ve O. Mukhtarov, “Comparison Theorems for One Sturm-Liouville Problem with Nonlocal Boundary Conditions”, TJMCS, c. 10, ss. 121–125, 2018.
ISNAD Aydemir, Kadriye vd. “Comparison Theorems for One Sturm-Liouville Problem With Nonlocal Boundary Conditions”. Turkish Journal of Mathematics and Computer Science 10 (Aralık 2018), 121-125.
JAMA Aydemir K, Olğar H, Mukhtarov O. Comparison Theorems for One Sturm-Liouville Problem with Nonlocal Boundary Conditions. TJMCS. 2018;10:121–125.
MLA Aydemir, Kadriye vd. “Comparison Theorems for One Sturm-Liouville Problem With Nonlocal Boundary Conditions”. Turkish Journal of Mathematics and Computer Science, c. 10, 2018, ss. 121-5.
Vancouver Aydemir K, Olğar H, Mukhtarov O. Comparison Theorems for One Sturm-Liouville Problem with Nonlocal Boundary Conditions. TJMCS. 2018;10:121-5.