Small solutions of linear autonomous functional differential equations

DOI10.1016/0022-0396(70)90021-5zbMath0228.34044OpenAlexW2042684791MaRDI QIDQ2549802

Daniel B. Henry

Publication date: 1970

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(70)90021-5

Mathematics Subject Classification ID

Asymptotic theory of functional-differential equations (34K25) Linear ordinary differential equations and systems (34A30)

Related Items (30)

Oscillation theory of linear systems ⋮ Computer control for low-order time-delay systems† ⋮ Series expansions for functional differential equations ⋮ Necessary and sufficient conditions for oscillation of the solutions of linear functional differential equations of neutral type with distributed delay ⋮ Pointwise completeness and degeneracy of functional differential equations in Banach spaces. I: General time delays ⋮ Morse decompositions for delay-differential equations ⋮ Characterization of small solutions in functional differential equations ⋮ Abnormal solutions of evolution equations ⋮ Individual asymptotics of \(C_0\)-semigroups: Lower bounds and small solutions ⋮ On small solutions of delay equations in infinite dimensions ⋮ A maximum principle for optimal control problems with neutral functional differential systems ⋮ The structural operator F and its role in the theory of retarded systems ⋮ The structural operator F and its role in the theory of retarded systems. II ⋮ On growth and decay of solutions of perturbed retarded linear equations ⋮ A review of some subtleties of practical relevance for time-delay systems of neutral type ⋮ An algebraic characterization of closed small attainability subspaces of delay systems ⋮ Observability and related structural results for linear hereditary systems† ⋮ Observability and detectability of linear time-delay systems with unknown disturbances ⋮ Behavior near constant solutions of functional differential equations ⋮ Invariant manifolds for singularly perturbed linear functional differential equations ⋮ The numerical solution of forward-backward differential equations: decomposition and related issues ⋮ Projection series for retarded functional differential equations with applications to optimal control problems ⋮ Degenerate difference-differential equations: Algebraic theory ⋮ Completeness and F-completeness of eigenfunctions associated with retarded functional differential equations ⋮ The discrete Lyapunov function for scalar differential delay equations ⋮ Forward and backward continuation for neutral functional differential equations ⋮ The degeneracy property in linear autonomous functional differential equations of the neutral type ⋮ Observability of nontrivial small solutions for neutral systems ⋮ Characterising small solutions in delay differential equations through numerical approximations ⋮ Optimal control of linear retarded systems to small solutions

Cites Work

• Backward existence and uniqueness for retarded functional differential equations
• A folk theorem in functional differential equations
• The adjoint of a linear functional differential equation and boundary value problems
• A FLOQUET THEORY FOR FUNCTIONAL DIFFERENTIAL EQUATION
• AN EXAMPLE IN THE THEORY OF THE SPECTRUM OF A FUNCTION
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