Bounded solutions of linear and weakly nonlinear differential equations in a Banach space with an unbounded operator in the linear part

DOI10.1134/S0012266112060055zbMath1275.34084MaRDI QIDQ1760474

Oleksander Pokutnyi

Publication date: 14 November 2012

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

zbMATH Keywords

generalized inverse equationweak bounded solutionweakly nonlinear differential equations

Mathematics Subject Classification ID

Nonlinear differential equations in abstract spaces (34G20) Growth and boundedness of solutions to ordinary differential equations (34C11) Linear differential equations in abstract spaces (34G10) Dichotomy, trichotomy of solutions to ordinary differential equations (34D09)

Related Items (5)

The Gelfand-Shilov type estimate for Green's function of the bounded solutions problem ⋮ Exponential dichotomy and bounded solutions of differential equations in the Fréchet space ⋮ Boundary-value problems for differential equations in Banach spaces with unbounded operator in the linear part ⋮ Spectral analysis of differential operators with unbounded operator coefficients on the half-line ⋮ Representation of the solutions of boundary-value problems for the Schrödinger equation in a Hilbert space

Cites Work

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• Geometric theory of semilinear parabolic equations
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• Evolution equations: Dichotomies and the Fredholm alternative for bounded solutions
• Bounded solutions of linear differential equations in a Banach space
• Spectral analysis of differential operators with unbounded operator-valued coefficients, difference relations and semigroups of difference relations

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