Stability of solutions to the Cauchy problem with respect to linear approximation, and branching equation in the root subspace
DOI10.1134/S0081543812060247zbMath1315.34066OpenAlexW2091452180MaRDI QIDQ744301
V. A. Trenogin, Boris Vladimirovich Loginov, Luisa Revmirovna Kim-Tyan
Publication date: 7 October 2014
Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1134/s0081543812060247
local Lipschitz conditionsemilinear Cauchy problemclosed linear Fredholm operatorlinear Cauchy problem
Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Nonlinear differential equations in abstract spaces (34G20) Stability of solutions to ordinary differential equations (34D20) Linear differential equations in abstract spaces (34G10)
Cites Work
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- The Lyapunov theorem on stability with respect to linear approximation as a corollary to the implicit operator theorem
- Linear approximations for differential equations in Banach spaces and Lyapunov stability
- Generalized Jordan structure in the problem of the stability of bifurcating solutions
- Branching equation in the root subspace
- Interlaced branching equations in the theory of non-linear equations
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