A Study of the Rigidity of Descriptor Dynamical Systems in a Banach Space
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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.
KeywordsBanach Space Cauchy Problem Coker Fredholm Operator Limit Equation
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- 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
- 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.M. M. Vainberg and V. A. Trenogin, Theory of Branching of Solutions of Nonlinear Equations [in Russian], Nauka, Moscow (1969).Google Scholar
- 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.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.S. G. Krein, Linear Equations in Banach Spaces [in Russian], Nauka, Moscow (1967); English transl.: Birkhäuser, Boston etc. (1982).Google Scholar
- 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