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Sturm–Liouville Problems

  • Gianpietro Elvio CossaliEmail author
  • Simona Tonini
Chapter
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Part of the Mathematical Engineering book series (MATHENGIN)

Abstract

In Chap.  3 we have seen how the separability of PDEs leads to ordinary differential equations problems, usually of second order. The problem is complemented with B.C.s and the reduction of the initial PDE to second order ODEs often yield a so-called Sturm–Liouville (SL) problem (named after the French mathematicians Jacques Charles François Sturm, 1803–1855, and Joseph Liouville, 1809–1882).

References

  1. 1.
    Davis, H.F.: Fourier Series and Orthogonal Functions. Dover, New York (1989)Google Scholar
  2. 2.
    Strang, G.: The fundamental theorem of linear algebra. Am. Math. Month. 100(9), 848–855 (1993)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Olver, F.W., Lozier, D.W., Boisvert, R.F., Clark, C.W. (eds.): NIST Handbook of Mathematical Functions. Cambridge University Press, Cambridge (2010)Google Scholar
  4. 4.
    Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 10th edn. Dover Publications Inc., United States (1972)Google Scholar
  5. 5.
    Kreyszig, E.: Introductory Functional Analysis with Applications. Wiley, New York (1978)Google Scholar
  6. 6.
    Arfken, G.B., Weber, H.J.: Mathematical Methods for Physicists. Elsevier Academic Press, Cambridge (2005)Google Scholar
  7. 7.
    Rudin, W.: Functional Analysis. Mc Graw Hill, New York (1991)Google Scholar
  8. 8.
    Al-Gwaiz, M.A.: Sturm-Liouville Theory and its Applications. Springer, Berlin (2008)Google Scholar
  9. 9.
    Zettl, A.: Sturm-Liouville Theory. American Mathematical Society, Providence (2010)Google Scholar
  10. 10.
    Ince, L.: Ordinary Differential Equations. Dover, Illinois (1956)Google Scholar
  11. 11.
    Tenenbaum, M., Pollard, H.: Ordinary Differential Equations. Dover, Illinois (1985)Google Scholar
  12. 12.
    Lebedev, N.N.: Special Functions and Their Applications. Dover, Illinois (1972)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2021

Authors and Affiliations

  1. 1.Department of Engineering and Applied SciencesUniversity of BergamoDalmineItaly

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