Journal of Mathematical Sciences

, Volume 208, Issue 1, pp 131–138 | Cite as

A Study of the Rigidity of Descriptor Dynamical Systems in a Banach Space

  • S. P. Zubova
  • E. B. Raetskaya

We consider an equation in a Banach space that is unsolvable with respect to derivative with perturbation on the right-hand side of the equation, realized by a small the parameter. We find the rigidity condition of the dynamical system and the conditions under which the zero value of parameter is a bifurcation point. Bibliography: 8 titles.


Banach Space Cauchy Problem Coker Fredholm Operator Limit Equation 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P. L. Gristiansen, V. Mito, and P. S. Lomdahl, “On a Toda lattice model with a transversal degree of freedom,” Nonlinearity, No 4, 477–501 (1990).Google Scholar
  2. 2.
    G. A. Sviridyuk and V. E. Fedorov, Linear Sobolev Type Equations and Degenerate Semigroups of Operators, USP, Utrecht etc. (2003).MATHCrossRefGoogle Scholar
  3. 3.
    Nguyen Khac Diep and V. F. Chistyakov, “Using partial differential algebraic equations in modelling” [in Russian], Vestn. Yuzhno-Ural. Gos. Univ., Ser. Mat. Model. Program. 6, No. 1, 98–109 (2013).Google Scholar
  4. 4.
    M. M. Vainberg and V. A. Trenogin, Theory of Branching of Solutions of Nonlinear Equations [in Russian], Nauka, Moscow (1969).Google Scholar
  5. 5.
    F. V. Atkinson, “Normal solvability of linear equations in normed spaces” [in Russian], Mat. Sb. 28, No. 1, 3–14 (1951).Google Scholar
  6. 6.
    S. P. Zubova, “Solution of the homogeneous Cauchy problem for an equation with a Fredholm operator multiplying the derivative” [in Russian], Dokl. Akad. Nauk, Ross. Akad. Nauk 428, No. 4, 444-446 (2009); English transl.: Dokl. Math. 80, No. 2, 710-712 (2009).Google Scholar
  7. 7.
    S. G. Krein, Linear Equations in Banach Spaces [in Russian], Nauka, Moscow (1967); English transl.: Birkhäuser, Boston etc. (1982).Google Scholar
  8. 8.
    E. V. Raetskaya, “On study of the behavior of the solution to a singularly perturbed equation” [in Russian], Dep. VINITI No. 10392 (2002).Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Voronezh State UniversityVoronezhRussia
  2. 2.Voronezh State Forest Technical AcademyVoronezhRussia

Personalised recommendations