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Differential and Difference Equations with Applications pp 457–464Cite as

On Estimates of the First Eigenvalue for the Sturm–Liouville Problem with Symmetric Boundary Conditions and Integral Condition

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 47))

Abstract

We consider the Sturm–Liouville problem with symmetric boundary conditions and an integral condition. We estimate the first eigenvalue \(\lambda _{1}\) of this problem for different values of the parameters.

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References

  1. Courant, R., Hilbert, D.: Methods of Mathematical Physics, vol. 1 and 2, p. 560. Wiley, New York (1989)

    Google Scholar 

  2. Egorov, Yu., Kondratiev, V.: On spectral theory of elliptic operators (English). Operator Theory: Advances and Applications, vol. 89, p. 328. Birkhauser, Basel (1996)

    Google Scholar 

  3. Ezhak, S.S.: On the estimates for the minimum eigenvalue of the Sturm–Liouville problem with integral condition (English). J. Math. Sci. New York 145(5), 5205–5218 (2007); translation from Sovrem. Mat. Prilozh. 36, 56–69 (2005)

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  4. Karulina, E.: Some estimates for the first eigenvalue of the Sturm–Liouville problem with symmetric boundary conditions. Proceedings of the International miniconference of Qualitative Theory of Differential Equations and Applications, pp. 116–123. MESI, Moscow (2010). ISBN:978-5-7764-0607-2

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  5. Karulina, E.: Some estimates for the minimal eigenvalue of the Sturm–Liouville problem with third-type boundary conditions. J. Math. Bohemica, Praha, Czech Republic 136(4), 377–384 (2011)

    Google Scholar 

  6. Muryshkina, O.V.: On estimates for the first eigenvalue of the Sturm–Liouville problem with symmetric boundary conditions (Russian). Vestnik Molodyh Uchenyh. – 3’2005. Series: Applied mathematics and Mechanics. – 1’2005, p. 36–52

    Google Scholar 

  7. Vinokurov, V.A., Sadovnichii, V.A.: On the range of variation of an eigenvalue when the potential is varied (English. Russian original). Dokl. Math. 68(2), 247–252 (2003); translation from Dokl. Ross. Akad. Nauk 392(5), 592–597 (2003)

    Google Scholar 

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Authors and Affiliations

  1. Moscow State University of Economics, Statistics and Informatics, Nezhinskaya str. 7, Moscow, Russia

    Elena Karulina

Authors
  1. Elena Karulina
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Correspondence to Elena Karulina .

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Editors and Affiliations

  1. Departamento de Ciências Exactas e Naturais, Academia Militar, Amadora, Portugal

    Sandra Pinelas

  2. University of Zürich Institute of Mathematics, Zürich, Switzerland

    Michel Chipot

  3. Masaryk University Dept. Mathematics, Brno, Czech Republic

    Zuzana Dosla

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Karulina, E. (2013). On Estimates of the First Eigenvalue for the Sturm–Liouville Problem with Symmetric Boundary Conditions and Integral Condition. In: Pinelas, S., Chipot, M., Dosla, Z. (eds) Differential and Difference Equations with Applications. Springer Proceedings in Mathematics & Statistics, vol 47. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7333-6_40

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