The source function of the chain of rods with elastic supports

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Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system's guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	DOI: 10.23671/VNC.2016.2.7388 The source function of the chain of rods with elastic supports Kulaev R. Ch. Vladikavkaz Mathematical Journal 2014. Vol. 16. Issue 2. Abstract: We consider a boundary value problem for a fourth-order equation modeling elastic deformations of a rod system with elastic supports. The Green's function of the boundary value problem with elastic supports expressed through the Green's function of the boundary value problem without supports. Keywords: fourth-order equation, discontinuous boundary value problem, Green's function Language: Russian Download the full text For citation: Kulaev R. Ch. The source function of the chain of rods with elastic supports. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 16, no. 2, pp.49-61. DOI 10.23671/VNC.2016.2.7388 + References 1. Pokornyj Ju. V., Penkin O. M., Prjadiev V. L., Borovskih A. V., Lazarev K. P., Shabrov S. A. Differencial'nye Uravnenija na Geometricheskih Grafah, Moskva, Fizmatlit, 2007, 272 p. (Russian). 2. Pokornyj Ju. V., Bahtina Zh. I., Zvereva M. B., Shabrov S. A. Oscilljacionnyj Metod Shturma v Spektral'nyh Zadachah, Moskva, Fizmatlit, 2009, 192 p. (Russian). 3. Pokornyj Ju. V. O znakoreguljarnyh funkcijah Grina nekotoryh neklassicheskih zadach. Uspehi Mat. Nauk, 1981, vol. 36, no. 4, pp. 205-206 (Russian). 4. Pokornyj Ju. V., Borovskih A. V. Chebyshev-Haar systems in the theory of discontinuous Kellogg kernels. Russian Math. Surveys, 1994, vol. 49, no. 3, pp. 1-42. 5. Borovskih A. V., Lazarev K. P., Pokornyj Ju. V. Oscillatory spectral properties of discontinuous boundary value problems. Dokl. Math., 1994, vol. 49, no. 2, pp. 328-333. 6. Borovskih A. V., Lazarev K. P., Pokornyj Ju. V. On the Kellogg kernels in discontinuous problems. Proc. Steklov Institute Math., 1995, vol. 211, pp. 92-108. 7. Pokornyj Ju. V., Lazarev K. P. Some oscillation theorems for multipoint problems. Differ. Uravn. [Differ. Equations], 1987, vol. 23, no. 4, pp. 658-670 (Russian). 8. Borovskih A. V. Sign regularity conditions for discontinuous boundary-value problems. Math. Notes, 2003, vol. 74, no. 5, pp. 607-618. 9. Levin A. Ju., Stepanov G. D. One-dimensional boundary value problems with operators that do not lower the number of sign alternations, II. Sib. Mat. Zhurn. [Sib. Math. J.], 1976, vol. 17, no. 4, pp. 813-830 (Russian). 10. Teptin A. L. K voprosu ob oscilljacionnosti spektra mnogotochechnoj kraevoj zadachi. Izv. Vuzov. Matematika, 1999, no. 4 (443), pp. 44-53 (Russian). 11. Pokornyj Ju. V. Zeros of the Green's function for the de la Vallée-Poussin problem. Sbornik: Mathematics, 2008, vol. 199, no. 6, pp. 891-921. 12. Derr V. Ja. On the generalized de la Vallee-Poussin problem. Differ. Uravn. [Differ. Equations], 1987, vol. 23, no. 11, pp. 1861-1872 (Russian). 13. Kulaev R. Ch. O znakoreguljarnosti funkcii Grina dlja uravnenija chetvertogo porjadka. Differ. Uravn. [Differ. Equations], 2013, vol. 49, no. 6, pp. 813-814 (Russian). 14. Lankaster P. Teorija Matric [The Theory of Matrices], Moskva, Nauka, 1978, 280 p. (Russian). 15. Gantmaher F. R. Teorija Matric [The Theory of Matrices], Moskva, Nauka, 1966, 576 p. (Russian). 16. Stepanov G. D. Effective criteria for the strong sign-regularity and the oscillation property of the Green's functions of two-point boundary-value problems. Sbornik: Mathematics, 1997, vol. 188, no. 11, pp. 1687-1728. 17. Bratus' A. S., Sejranjan A. P. Dostatochnye uslovija jekstremuma v zadachah optimizacii sobstvennyh znachenij. Prikl. Mat. i Meh., 1984, no. 4, pp. 657-667 (Russian). 18. Banichuk N. V. Vvedenie v Optimizaciju Konstrukcij, Moskva, Nauka, 1986, 304 p. (Russian). 19. Masur E. F. Optimal structural design under multiple eigenvalue constraints. Int. J. Solids Struct., 1984, vol. 20, no. 3, pp. 211-231. The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses. ← Contents of issue


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