Reduction principle and dynamic behaviors for a class of partial functional differential equations

DOI10.1016/J.NA.2009.01.008zbMath1178.34097OpenAlexW2018134341MaRDI QIDQ1030065

Mostafa Adimy, Khalil Ezzinbi, Abdelhai El Azzouzi

Publication date: 1 July 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2009.01.008

zbMATH Keywords

mild solutionspectral decompositionanalytic semigroupfunctional differential equationfractional power of operatorsvariation of constants formulaalmost automorphic solutionreduction principle

Mathematics Subject Classification ID

Almost and pseudo-almost periodic solutions to functional-differential equations (34K14) Functional-differential equations in abstract spaces (34K30) Almost and pseudo-almost periodic solutions to PDEs (35B15) General theory of functional-differential equations (34K05) Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions (43A60)

Related Items (9)

Periodic solution for some class of linear partial differential equation with infinite delay using semi-Fredholm perturbations ⋮ \(C^{(n)}\)-almost periodic and \(C^{(n)}\)-almost automorphic solutions for a class of partial functional differential equations with finite delay ⋮ Unnamed Item ⋮ Pseudo-almost Periodic Solutions of Class r in the α-Norm Under the Light of Measure Theory ⋮ Analytical solutions for multi-term time-space coupling fractional delay partial differential equations with mixed boundary conditions ⋮ Unnamed Item ⋮ Pseudo almost automorphic solutions of class \(r\) in \(\alpha\)-norm under the light of measure theory ⋮ Variation of constants formula and reduction principle for a class of partial functional differential equations with infinite delay ⋮ Stepanov ergodic perturbations for some neutral partial functional differential equations

Cites Work

• Unnamed Item
• Existence and stability in the \(\alpha\)-norm for partial functional differential equations of neutral type
• A Massera type theorem for almost automorphic solutions of differential equations
• Variation of constants formula and almost periodic solutions for some partial functional differential equations with infinite delay
• Almost automorphic solutions for some partial functional differential equations
• Bohr--Neugebauer type theorem for some partial neutral functional differential equations
• Almost automorphic mild solutions to some partial neutral functional-differential equations and applications
• Semigroups of linear operators and applications to partial differential equations
• Almost periodic differential equations
• Partial differential equations with deviating arguments in the time variable
• A variation of constants formula for an abstract functional differential equation of retarded type
• Invariant manifolds of partial functional differential equations.
• A variation-of-constants formula for abstract functional differential equations in the phase space
• Theory and applications of partial functional differential equations
• Existence results for partial neutral functional integrodifferential equations with unbounded delay
• Almost automorphic solutions for partial functional differential equations with infinite delay
• Behavior near hyperbolic stationary solutions for partial functional differential equations with infinite delay
• The existence of periodic solutions of systems of differential equations
• Existence, Stability, and Compactness in the α-Norm for Partial Functional Differential Equations
• Existence and Stability for Partial Functional Differential Equations

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