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Higher-Order Differential Equations Having a Singularity in an Interior Point

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Abstract

Ordinary differential equations of an arbitrary order having a non-integrable singularity inside the interval are considered under additional matching conditions for solutions at the singular point. We construct special fundamental systems of solutions for this class of differential equations, study their asymptotical, analytical and structural properties and the behavior of the corresponding Stokes multipliers. These fundamental systems of solutions are used in spectral analysis of differential operators with singularities.

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References

  1. Naimark M.A., Linear Differential Operators, 2nd ed., “Nauka” Moscow 1969; English transi. of 1st ed., Parts 1,11, Ungar, New York 1967, 1968.

    Google Scholar 

  2. Kostjuchenko A.G. and Sargsjan I.S., Distribution of Eigenvalues. Selfadjoint Ordinary Differential Operators, Nauka, Moscow, 1979.

    Google Scholar 

  3. Beals R., Deift P. and Tomei C, Direct and Inverse Scattering on the Line, Math. Surveys and Monographs, v. 28, Amer. Math. Soc. Providence: RI, 1988.

    Google Scholar 

  4. Yurko V.A., Inverse Spectral Problems for Differential Operators and their Applications, Gordon and Breach, New York, 2000.

  5. Yurko V.A., Integral transforms connected with differential operators having singularities inside the interval, Integral Transforms and Special Functions 5 (1997), no. 3–4, 309–322.

    Article  MathSciNet  Google Scholar 

  6. Yurko V.A., Inverse problems for differential equations with singularities lying inside the interval, Journal of Inverse and Ill-Posed Problems, vol. 8, no. 1 (2000), 89–103.

    MathSciNet  MATH  Google Scholar 

  7. Yurko V.A., Inverse problem for differential equations with a singularity, Differ. Uravneniya 28 (1992), 1355–1362; English transi. in Differential Equations 28 (1992), 1100–1107.

    MathSciNet  MATH  Google Scholar 

  8. Yurko V.A., On boundary value problems with a singularity and jump conditions inside the interval, Inter. Symposium of Math., Kazakhstan-2000, Almaty, 2000, pp. 50–51.

  9. Bellman R. and Cooke K., Differential-difference Equations, Academic Press, New York, 1963.

    MATH  Google Scholar 

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  1. Department of Mathematics, Saratov State University, Astrakhanskaya 83, Saratov, 410026, Russia

    Vjacheslav Yurko

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  1. Vjacheslav Yurko
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Correspondence to Vjacheslav Yurko.

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Yurko, V. Higher-Order Differential Equations Having a Singularity in an Interior Point. Results. Math. 42, 177–191 (2002). https://doi.org/10.1007/BF03323562

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  • DOI: https://doi.org/10.1007/BF03323562

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