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Differential Equations

, Volume 46, Issue 2, pp 284–288 | Cite as

A priori estimates and solvability of the third two-point boundary value problem

  • A. N. Naimov
  • M. V. Bystretskii
Short Communications
  • 38 Downloads

Abstract

We study a priori estimates and solvability of a nonlinear two-point boundary value problem for systems of second-order ordinary differential equations with leading positively homogeneous nonlinearity of order > 1 vanishing on a single surface. Assuming that an a priori estimate holds, we prove the invariance of the solvability of the problem under a continuous change of the leading nonlinear homogeneous terms and under arbitrary perturbations that do not affect the behavior of the leading nonlinear homogeneous terms at infinity.

Keywords

Continuous Change Nonsingular Matrix Nonzero Solution Periodic Problem Single Surface 
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

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    Naimov, A.N. and Khakimov, R.I., On the Solvability of a Certain Nonlinear Periodic Problem, Dokl. Akad. Nauk Resp. Tajikistan, 2001, vol. 44, no. 3, pp. 35–40.Google Scholar
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    Naimov, A.N., On the Theory of Two-Point Boundary Value Problems for Systems of Nonlinear Ordinary Differential Equations, Dokl. Akad. Nauk Resp. Tajikistan, 1998, vol. 41, no. 9, pp. 30–34.Google Scholar
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    Naimov, A.N., On the Solvability of the Third Nonlinear Two-Point Boundary Value Problem on the Plane, Differ. Uravn., 2002, vol. 38, no. 1, pp. 132–133.MathSciNetGoogle Scholar
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    Mukhamadiev, E.M. and Naimov, A.N., On the Theory of Two-Point Boundary Value Problems for Second-Order Differential Equations, Differ. Uravn., 1999, vol. 35, no. 10, pp. 1372–1381.MathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • A. N. Naimov
    • 1
    • 2
  • M. V. Bystretskii
    • 1
    • 2
  1. 1.Vologda State Technical UniversityVologdaRussia
  2. 2.Vologda State Pedagogical UniversityVologdaRussia

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