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Differential Equations

, Volume 46, Issue 2, pp 182–186 | Cite as

On boundary value problems for an nth-order equation

  • N. I. Vasil’ev
  • A. Ya. Lepin
  • L. A. Lepin
Ordinary Differential Equations
  • 54 Downloads

Abstract

For an nth-order differential equation with right-hand side satisfying the Carathéodory conditions, we consider a two-point boundary value problem with boundary conditions of which the first two have a general form and the remaining conditions are simplest. We show that the existence of a lower and an upper function and the compactness condition imply the solvability of this boundary value problem.

Keywords

Compactness Condition Nonlinear Boundary Monotonicity Condition Nonlinear Boundary Condition Odory Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Vasil’ev, N.I. and Klokov, Yu.A., Osnovy teorii kraevykh zadach obyknovennykh differentsial’nykh uravnenii (Foundations of the Theory of Boundary Value Problems for Ordinary Differential Equations), Riga: Zinatne, 1978, pp. 5–181.Google Scholar
  2. 2.
    Kiguradze, I.T., Boundary Value Problems for Systems of Ordinary Differential Equations, Itogi Nauki Tekhn. Sovrem. Probl. Mat. Noveish. Dostizh., 1987, vol. 30, pp. 3–103.MathSciNetGoogle Scholar
  3. 3.
    Lepin, A.Ya. and Lepin, L.A., Kraevye zadachi dlya obyknovennogo differentsial’nogo uravneniya vtorogo poryadka (Boundary Value Problems for a Second-Order Ordinary Differential Equation), Riga: Zinatne, 1988.zbMATHGoogle Scholar
  4. 4.
    Zhao Weili, Existence and Uniqueness of Solutions for Third Order Nonlinear Boundary Value Problems, Tohoku Math. J., 1992, vol. 44, pp. 545–555.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Rozov, N.Kh. and Sushko, V.G., The Method of Barrier Functions and Asymptotic Solutions of Singularly Perturbed Boundary Value Problems, Dokl. Akad. Nauk, 1993, vol. 332, no. 3, pp. 150–152.Google Scholar
  6. 6.
    Klokov, Yu.A., On Two-Point Problems for Third-Order Ordinary Differential Equations, Differ. Uravn., 2003, vol. 39, no. 4, pp. 557–559.MathSciNetGoogle Scholar
  7. 7.
    Klokov, Yu.A., On Upper and Lower Functions for a Fourth-Order Ordinary Differential Equation. I, Differ. Uravn., 2005, vol. 41, no. 8, pp. 1074–1083.MathSciNetGoogle Scholar
  8. 8.
    Minhos, F., Gyulov, T., and Santos, A.I., Existence and Location Result for a Fourth Order Boundary Value Problem, Discrete Contin. Dyn. Syst. Suppl. Vol., 2005, pp. 662–671.Google Scholar
  9. 9.
    Minhos, F., Santos, A.I., and Gyulov, T., A Fourth-Order BVP of Sturm-Liouville Type with Asymmetric Unbounded Nonlinearities, Proc. Conf. Diff. and Difference Equ. and Appl., 2005, pp. 795–804.Google Scholar
  10. 10.
    Minhos, F., Gyulov, T., and Santos, A.I., On an Elastic Beam Fully Equation with Nonlinear Boundary Conditions, Proc. Conf. Diff. and Difference Equ. and Appl., 2005, pp. 805–814.Google Scholar
  11. 11.
    Minhos, F. and Santos, A.I., Existence and Non-Existence Results for Two-Point Boundary Value Problems of Higher Order, in Int. Conf. Diff. Equ., Hasselt, 2003, pp. 249–251.Google Scholar
  12. 12.
    Lepin, A.Ya. and Lepin, L.A., A Boundary Value Problem for an nth-Order Equation, in Nauchnye Tr. (Scientific Papers), Riga, 2006, pp. 24–27.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • N. I. Vasil’ev
    • 1
  • A. Ya. Lepin
    • 1
  • L. A. Lepin
    • 1
  1. 1.Institute of Mathematics and Computer ScienceUniversity of LatviaRigaLatvia

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