Spectral methods for studying degenerate differential-operator equations. I.

DOI10.1007/S10958-007-0267-2zbMath1188.34079OpenAlexW2023736359MaRDI QIDQ1040295

Anatoliy Rutkas

Publication date: 24 November 2009

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-007-0267-2

zbMATH Keywords

Laplace transforminfinite-dimensional systemsdifferential-algebraic equations

Mathematics Subject Classification ID

Implicit ordinary differential equations, differential-algebraic equations (34A09) Nonlinear differential equations in abstract spaces (34G20) Laplace transform (44A10) General theory of linear operators (47A99)

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On a Differential Game in a System Described by a Functional Differential Equation ⋮ Stochastic optimal control of a descriptor system ⋮ Decomposition of descriptor control systems ⋮ Fundamental solution of an implicit linear inhomogeneous first order differential equation over an arbitrary ring ⋮ Fundamental solution of the simplest implicit linear differential equation in a vector space

Cites Work

• Degenerate and singular evolution equations in Banach space
• Perturbations of Skew-Hermitian bundles and the degenerate Cauchy problem
• Solvability and completeness for an electrodynamical systems that is not of Kovalevskaya type
• Uniqueness and approximation theorems for a degenerate operator-differential equation
• Some results concerning the abstract degenerate nonlinear equation \(D_ tMu(t)+Lu(t)=f(t,Ku(t))\)
• On solvability of degenerate nonstationary differential-difference equations in Banach spaces
• Existence and uniqueness of solutions of some abstract degenerate nonlinear equations
• Pairs of non self-adjoint operators and operator hypernodes
• Graphical Comparison of Covariance Matrices
• Implicit operator differential equations and applications to electrodynamics
• On some abstract degenerate problems of parabolic type—2. The nonlinear case
• Existence and uniqueness theorems for an implicit delay differential equation
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