Almost automorphic solutions to nonautonomous semilinear evolution equations in Banach spaces

DOI10.1016/j.na.2010.05.006zbMath1192.43005OpenAlexW2037936299MaRDI QIDQ984109

Ti-Jun Xiao, Hui-Sheng Ding, Jin Liang

Publication date: 13 July 2010

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.2010.05.006

zbMATH Keywords

evolution familysemilinear evolution equationpseudo-almost automorphicalmost automorphicStepanov-like almost automorphic

Mathematics Subject Classification ID

Nonlinear differential equations in abstract spaces (34G20) Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions (43A60)

Related Items (32)

Weighted piecewise pseudo almost automorphic functions with applications to abstract impulsive \(\nabla\)-dynamic equations on time scales ⋮ On completeness of the space of weighted Stepanov-like pseudo almost automorphic (periodic) functions ⋮ Besicovitch almost automorphic solutions of nonautonomous differential equations of first order ⋮ Symmetric-periodic solutions for some types of generalized neutral equations ⋮ Stepanov-like weighted asymptotic behavior of solutions to some stochastic differential equations in Hilbert spaces ⋮ Stepanov type \(\mu\)-pseudo almost automorphic mild solutions of semilinear fractional integrodifferential equations ⋮ Compact almost automorphic solutions for semilinear parabolic evolution equations ⋮ Unnamed Item ⋮ New composition theorems of Stepanov-like weighted pseudo almost automorphic functions and applications to nonautonomous evolution equations ⋮ Weighted Stepanov-like pseudo almost automorphy and applications ⋮ Composition of Stepanov-like pseudo almost automorphic functions and applications to nonautonomous evolution equations ⋮ Asymptotically almost automorphic solutions to nonautonomous semilinear evolution equations ⋮ Square-mean almost automorphic mild solutions to some stochastic differential equations in a Hilbert space ⋮ EXISTENCE OF <i>µ</i>-PSEUDO ALMOST AUTOMORPHIC SOLUTIONS TO ABSTRACT PARTIAL NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY ⋮ Almost automorphic mild solutions to neutral parabolic nonautonomous evolution equations with nondense domain ⋮ Translation invariance and related properties of \(\mu\)-pseudo almost automorphic (periodic) functions with application ⋮ Square-mean almost automorphic solution of a stochastic cellular neural network on time scales ⋮ Generalized almost automorphic and generalized asymptotically almost automorphic solutions of abstract Volterra integro-differential inclusions ⋮ Existence of pseudo-almost automorphic solutions for nonlinear differential equations ⋮ Almost automorphic solutions of non-autonomous differential equations ⋮ Unnamed Item ⋮ Pseudo-almost automorphic mild solutions to semilinear integral equations in a Banach space ⋮ Almost automorphic solutions to abstract fractional differential equations ⋮ Composition theorems of Stepanov almost periodic functions and Stepanov-like pseudo-almost periodic functions ⋮ Almost automorphic solutions to abstract Volterra equations on the line ⋮ Stability and approximation of almost automorphic solutions on time scales for the stochastic Nicholson's blowflies model ⋮ Compositions of pseudo almost automorphic functions via measure theory and applications ⋮ Existence of \(P\)-mean almost periodic mild solution for fractional stochastic neutral functional differential equation ⋮ Some new results on bounded solutions to a semilinear integro-differential equation in Banach spaces ⋮ Stepanov-like weighted pseudo almost automorphic solutions to fractional order abstract integro-differential equations ⋮ Unnamed Item ⋮ Pseudo almost automorphic mild solution of nonautonomous stochastic functional integro-differential equations

Cites Work

• Unnamed Item
• Evolution operators and strong solutions of abstract linear parabolic equations
• Weighted pseudo almost periodic functions and applications
• Existence and uniqueness of \(C^{(n)}\)-almost periodic solutions to some ordinary differential equations
• Pseudo almost automorphic solutions to semilinear differential equations in Banach spaces
• Almost automorphic mild solutions to some partial neutral functional-differential equations and applications
• Pseudo-almost-automorphic solutions to some neutral partial functional differential equations in Banach spaces
• Almost automorphic solutions of nonautonomous evolution equations
• Existence of pseudo-almost automorphic solutions to some abstract differential equations with \(\mathbf S^p\)-pseudo-almost automorphic coefficients
• Pseudo-almost automorphic mild solutions to nonautonomous differential equations and applications
• Mild pseudo-almost periodic solutions of nonautonomous semilinear evolution equations
• Almost automorphic solutions of certain abstract differential equations
• Dichotomies in stability theory
• Composition of pseudo almost automorphic and asymptotically almost automorphic functions
• Stepanov-like almost automorphic functions and monotone evolution equations
• Almost automorphic and pseudo-almost automorphic mild solutions to an abstract differential equation in Banach spaces
• Some properties of Stepanov-like almost automorphic functions and applications to abstract evolution equations
• Topics in Almost Automorphy
• Almost automorphic solutions of semilinear evolution equations
• A NEW APPROACH TO ALMOST PERIODICITY

This page was built for publication: Almost automorphic solutions to nonautonomous semilinear evolution equations in Banach spaces