Mathematical Notes

, Volume 63, Issue 6, pp 777–784 | Cite as

Smoothness of generalized solutions of boundary value problems for certain degenerate nonlinear ordinary differential equations

  • Yu. D. Salmanov


The variational method is applied to the study of a boundary value problem of the first kind for a class of nonlinear ordinary differential equations of order 2r with strong degeneracy at the endpoints of the interval (a, b). An inequality is obtained in which the norm of the solutionU of the problem under study in the sense ofW p, α r (a, b) is estimated from above by the norms of the given functions Φ(x) andF(x).

Key words

variational method boundary value problem of the first kind nonlinear ordinary differential equation Sobolev space coerciveness inequality 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. M. Nikol'skii,Approximation of Functions of Several Variables and the Embedding Theorem [in Russian], 2nd edition, Nauka, Moscow (1977).Google Scholar
  2. 2.
    P. I. Lizorkin and S. M. Nikol'skii, “The coercive property of elliptic equations with degeneracy. The variational method,”Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.],157, 90–118 (1981).MathSciNetGoogle Scholar
  3. 3.
    Yu. D. Salmanov, “Weighted function classes with degeneracy on manifolds of any dimension,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],294, No. 3, 539–542 (1987).MATHMathSciNetGoogle Scholar
  4. 4.
    Yu. D. Salmanov, “Traces of functions from weighted classes on manifolds and inverse embedding theorems,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],319, No. 4, 823–826 (1991).MATHGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • Yu. D. Salmanov
    • 1
  1. 1.N. Tusi Azerbaidzhan State UniversityAzerbaidzhan

Personalised recommendations