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On Basis Property for a Boundary-Value Problem with a Spectral Parameter in the Boundary Condition

Year 2006, Volume: 1 Issue: 5, 9 - 17, 01.04.2006

Abstract

References

  • T. J. Azizov, İ. C. İokhidov, OsnoniTteorii Lineynikh Operatoroc v Prostranstrax s Indedinitnoy Metrikoy (Linear Operators in Spaces With an Indefinite Metric) (Moscow: Nauka, 1986) (Russian)
  • P. A. Binding, P.J. Browne, K. Siddighi, ‘Sturm-Louville Problems with Eigenparameter Dependent Conditions’, Proc. Edinburgh Math. Soc. V.37, No.1 (1999), pp.57-72
  • P. A. Binding, P.J. Browne,B.A.Watson, ‘Sturm-Louville Problems with Boundary Conditions rationally dependent on the eigenparameter I’, Proc. Edinburg Math. Soc.45 (2002) pp, 631- 645.
  • P. A. Binding, P.J. Browne,B.A.Watson, ‘Sturm-Louville Problems with Boundary Conditions rationally dependent on the eigenparameter II’, Journal of Comp. and Appl. Math. 148 (2002), pp.147-168.
  • N. J. Guliyev, ‘Inverse Eigenvalue Problems for Sturm-Liouville Equations with Spectral Parameter Linearly Contained in one the Boundary Conditions’, Inverse Problems, 21 (2005) pp.1315-1330
  • C. T. Fulton, ‘Two-point Boundary Value Problems with Eigen-value Parameter Contained in the Boundary Conditions’ Proc. Roy. Soc. Edin., 77 A (1977), pp.293-308.
  • D. B. Hinton, ‘An Expansion Theorem for an Eigenvalue Problem with Eigenvalue Parameter in the Boundary Condition’, Quart. J. Math. Oxford, 30, No.2 (1979), pp.33-42
  • N. Yu. Kapustin, E. İ. Moisseev, ‘Spectral Problem with the Spectral Parameter in the Boundary Condition’, Diff. Equations . V. 33 No.1 (1997), pp.115-119
  • N. Yu. Kapustin, E. İ. Moisseev, ‘On the Spectral Problem from the Theory of the Parabolic Heat Equation’, Dok. Russ. Akad. Nauk, 352 No.4 (1997), pp.451-454
  • N. Yu. Kapustin, E. İ. Moisseev ‘Oscillation Properties of the Solutions to a Nonselfadjoint Spectral Parameter in the Boundary Condition’, Diff. Equations ., V. 35 No.8 (1999), pp.1024- 1027
  • N. Yu. Kapustin, , E. İ. Moisseev, ‘A remark On the Convergence problem for Spectral expansions Corresponding to Classical problem with a spectral Parameter in the Boundary Condition’, Diff. Equations, 37 V.(12) (2001), pp.1677-1683
  • N. B. Kerimov, V. S. Mirzoev, ‘On the Basis Properties of the One Spectral Problem with a Spectral Parameter in a Boundaray Condition’, Siberian Mathematical Journal, V.44, No.5 (2003), pp.813-816
  • N. B. Kerimov, Kh. R. Mamedov, ‘On a Boundary Value Problem with a Spectral Parameter in Boundary Conditions’, Siberian Mathematical Journal, V.40, No.2 (1999), pp.281-290
  • Kh. R. Mamedov, ‘On one Boundary Value Problem with Parameter in the Boundary Conditions’, Spektralmaya teoriya operatorov i prilojeniya, N.11 (1997), pp. 117-121
  • N. B. Kerimov, Kh. R. Mamedov, “The Sturm-Liouville Problem with Non-linear Spectral Parameter in the Boundary Conditions”, İzv.NAS Az., V.21, No 1 (2001), pp.100-104
  • Kh. R. Mamedov, ‘Uniqueness of Solution of the Scattering Theory with a Spectral Parameter in the Boundary Condition’, Math. Notes. 74, (1) (2003), pp.136-140
  • E. M. Russakovskij, ‘Operator treatment of boundary problems with spectral parameters entering via polynomials in the boundary conditions’, Funct. Anal. Appl. 9, (1975); pp.358-359 (translation from Funkts. Anal. i Prilozh. 9, No.4, (1975), pp.91-92) (Russian, English)
  • A. A. Shkalikov, ‘Boundary Value Problems for Ordinary Differential Equations with a Spectral Parameter in the Boundary Conditions’, Trudy Sem. İm. İ. G. Petrovsogo, V.9 (1983), pp.190- 229
  • A. N. Tikhonov, A. A. Samarskii, Equations of Mathematical Physics (Dover Books on Physics and Chemistry, 1990)
  • J. Walter, ‘Regular Eigenvalue Problems with Eigenvalue Parameter in the Boundary Conditions’, Math. Z., 133 (1973), pp. 301-312.

On Basis Property for a Boundary-Value Problem with a Spectral Parameter in the Boundary Condition

Year 2006, Volume: 1 Issue: 5, 9 - 17, 01.04.2006

Abstract

In the present work, the properties as completeness, minimality and basis property are investigated
for the eigenfunctions of Sturm-Liouville problem with a spectral parameter in the boundary condition

References

  • T. J. Azizov, İ. C. İokhidov, OsnoniTteorii Lineynikh Operatoroc v Prostranstrax s Indedinitnoy Metrikoy (Linear Operators in Spaces With an Indefinite Metric) (Moscow: Nauka, 1986) (Russian)
  • P. A. Binding, P.J. Browne, K. Siddighi, ‘Sturm-Louville Problems with Eigenparameter Dependent Conditions’, Proc. Edinburgh Math. Soc. V.37, No.1 (1999), pp.57-72
  • P. A. Binding, P.J. Browne,B.A.Watson, ‘Sturm-Louville Problems with Boundary Conditions rationally dependent on the eigenparameter I’, Proc. Edinburg Math. Soc.45 (2002) pp, 631- 645.
  • P. A. Binding, P.J. Browne,B.A.Watson, ‘Sturm-Louville Problems with Boundary Conditions rationally dependent on the eigenparameter II’, Journal of Comp. and Appl. Math. 148 (2002), pp.147-168.
  • N. J. Guliyev, ‘Inverse Eigenvalue Problems for Sturm-Liouville Equations with Spectral Parameter Linearly Contained in one the Boundary Conditions’, Inverse Problems, 21 (2005) pp.1315-1330
  • C. T. Fulton, ‘Two-point Boundary Value Problems with Eigen-value Parameter Contained in the Boundary Conditions’ Proc. Roy. Soc. Edin., 77 A (1977), pp.293-308.
  • D. B. Hinton, ‘An Expansion Theorem for an Eigenvalue Problem with Eigenvalue Parameter in the Boundary Condition’, Quart. J. Math. Oxford, 30, No.2 (1979), pp.33-42
  • N. Yu. Kapustin, E. İ. Moisseev, ‘Spectral Problem with the Spectral Parameter in the Boundary Condition’, Diff. Equations . V. 33 No.1 (1997), pp.115-119
  • N. Yu. Kapustin, E. İ. Moisseev, ‘On the Spectral Problem from the Theory of the Parabolic Heat Equation’, Dok. Russ. Akad. Nauk, 352 No.4 (1997), pp.451-454
  • N. Yu. Kapustin, E. İ. Moisseev ‘Oscillation Properties of the Solutions to a Nonselfadjoint Spectral Parameter in the Boundary Condition’, Diff. Equations ., V. 35 No.8 (1999), pp.1024- 1027
  • N. Yu. Kapustin, , E. İ. Moisseev, ‘A remark On the Convergence problem for Spectral expansions Corresponding to Classical problem with a spectral Parameter in the Boundary Condition’, Diff. Equations, 37 V.(12) (2001), pp.1677-1683
  • N. B. Kerimov, V. S. Mirzoev, ‘On the Basis Properties of the One Spectral Problem with a Spectral Parameter in a Boundaray Condition’, Siberian Mathematical Journal, V.44, No.5 (2003), pp.813-816
  • N. B. Kerimov, Kh. R. Mamedov, ‘On a Boundary Value Problem with a Spectral Parameter in Boundary Conditions’, Siberian Mathematical Journal, V.40, No.2 (1999), pp.281-290
  • Kh. R. Mamedov, ‘On one Boundary Value Problem with Parameter in the Boundary Conditions’, Spektralmaya teoriya operatorov i prilojeniya, N.11 (1997), pp. 117-121
  • N. B. Kerimov, Kh. R. Mamedov, “The Sturm-Liouville Problem with Non-linear Spectral Parameter in the Boundary Conditions”, İzv.NAS Az., V.21, No 1 (2001), pp.100-104
  • Kh. R. Mamedov, ‘Uniqueness of Solution of the Scattering Theory with a Spectral Parameter in the Boundary Condition’, Math. Notes. 74, (1) (2003), pp.136-140
  • E. M. Russakovskij, ‘Operator treatment of boundary problems with spectral parameters entering via polynomials in the boundary conditions’, Funct. Anal. Appl. 9, (1975); pp.358-359 (translation from Funkts. Anal. i Prilozh. 9, No.4, (1975), pp.91-92) (Russian, English)
  • A. A. Shkalikov, ‘Boundary Value Problems for Ordinary Differential Equations with a Spectral Parameter in the Boundary Conditions’, Trudy Sem. İm. İ. G. Petrovsogo, V.9 (1983), pp.190- 229
  • A. N. Tikhonov, A. A. Samarskii, Equations of Mathematical Physics (Dover Books on Physics and Chemistry, 1990)
  • J. Walter, ‘Regular Eigenvalue Problems with Eigenvalue Parameter in the Boundary Conditions’, Math. Z., 133 (1973), pp. 301-312.
There are 20 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Vagif Y. Gul, Khanlar R. Mamedov This is me

Khanlar R. Mamedov This is me

Publication Date April 1, 2006
Published in Issue Year 2006 Volume: 1 Issue: 5

Cite

APA Mamedov, V. Y. G. K. R. ., & Mamedov, K. R. (2006). On Basis Property for a Boundary-Value Problem with a Spectral Parameter in the Boundary Condition. Cankaya University Journal of Arts and Sciences, 1(5), 9-17.
AMA Mamedov VYGKR, Mamedov KR. On Basis Property for a Boundary-Value Problem with a Spectral Parameter in the Boundary Condition. Cankaya University Journal of Arts and Sciences. April 2006;1(5):9-17.
Chicago Mamedov, Vagif Y. Gul, Khanlar R., and Khanlar R. Mamedov. “On Basis Property for a Boundary-Value Problem With a Spectral Parameter in the Boundary Condition”. Cankaya University Journal of Arts and Sciences 1, no. 5 (April 2006): 9-17.
EndNote Mamedov VYGKR, Mamedov KR (April 1, 2006) On Basis Property for a Boundary-Value Problem with a Spectral Parameter in the Boundary Condition. Cankaya University Journal of Arts and Sciences 1 5 9–17.
IEEE V. Y. G. K. R. . Mamedov and K. R. Mamedov, “On Basis Property for a Boundary-Value Problem with a Spectral Parameter in the Boundary Condition”, Cankaya University Journal of Arts and Sciences, vol. 1, no. 5, pp. 9–17, 2006.
ISNAD Mamedov, Vagif Y. Gul, Khanlar R. - Mamedov, Khanlar R. “On Basis Property for a Boundary-Value Problem With a Spectral Parameter in the Boundary Condition”. Cankaya University Journal of Arts and Sciences 1/5 (April 2006), 9-17.
JAMA Mamedov VYGKR, Mamedov KR. On Basis Property for a Boundary-Value Problem with a Spectral Parameter in the Boundary Condition. Cankaya University Journal of Arts and Sciences. 2006;1:9–17.
MLA Mamedov, Vagif Y. Gul, Khanlar R. and Khanlar R. Mamedov. “On Basis Property for a Boundary-Value Problem With a Spectral Parameter in the Boundary Condition”. Cankaya University Journal of Arts and Sciences, vol. 1, no. 5, 2006, pp. 9-17.
Vancouver Mamedov VYGKR, Mamedov KR. On Basis Property for a Boundary-Value Problem with a Spectral Parameter in the Boundary Condition. Cankaya University Journal of Arts and Sciences. 2006;1(5):9-17.