Solvability on the real line of a class of linear Volterra integrodifferential equations of parabolic type

DOI10.1007/BF01761464zbMath0646.45013OpenAlexW1980312834MaRDI QIDQ1103813

Alessandra Lunardi, Giuseppe Da Prato

Publication date: 1988

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01761464

zbMATH Keywords

periodic solutionsBanach spaceanalytic semigroupbounded solutionsgeneralized spectrumabstract linear integrodifferential equationFredholm-like alternativelinear Volterra integrodifferential equations of parabolic type

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Abstract integral equations, integral equations in abstract spaces (45N05)

Related Items (20)

Existence results for some damped second-order Volterra integro-differential equations ⋮ Global existence for a semilinear parabolic Volterra equation ⋮ Hölder continuous solutions for integro-differential equations and maximal regularity ⋮ Differentiability of solutions of abstract neutral integro-differential equations ⋮ Infinite delay parabolic integro-differential equations with singular kernels ⋮ Existence and regularity results for an integral equation with infinite delay in a Banach space ⋮ Bounded mild solutions for semilinear integro differential equations in Banach spaces ⋮ Existence results in the \(\alpha \)-norm for neutral partial functional integro-differential equations with infinite delay ⋮ Optimal control for evolution equations with memory ⋮ Existence, global continuation and regularity in the \(\alpha\)-norm for some partial functional integrodifferential equations with infinite delay ⋮ Regularity of solutions of abstract retarded functional differential equations with unbounded delay ⋮ On a class of second order integrodifferential equations ⋮ Maximal regularity for perturbed integral equations on periodic Lebesgue spaces ⋮ Asymptotically almost periodic solutions for abstract partial neutral integro-differential equation ⋮ Existence results for neutral integro-differential equations with unbounded delay ⋮ Fractional resolvent operator with α ∈ (0,1) and applications ⋮ Existence results for partial neutral functional differential equations with unbounded delay ⋮ \(L^p\)-maximal regularity for a class of degenerate integro-differential equations with infinite delay in Banach spaces ⋮ 𝐶^{𝛼}-classical solutions for abstract non-autonomous integro-differential equations ⋮ Unnamed Item

Cites Work

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• Linear integro-differential equations in Banach spaces
• Thermodynamics and departures from Fourier's law of heat conduction
• Series Expansions for Resolvents of Volterra Integrodifferential Equations in Banach Space
• On Linear Volterra Equations of Parabolic Type in Banach Spaces
• Bounded Solutions of Volterra Equations
• Generation of Analytic Semigroups by Strongly Elliptic Operators Under General Boundary Conditions
• Volterra Integral Equations in Banach Space
• On kernels, eigenvalues, and eigenfunctions of operators related to elliptic problems
• On heat conduction in materials with memory
• Generation of Analytic Semigroups by Strongly Elliptic Operators

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