Differential and Integral Equations

Eberlein-weakly almost-periodic solutions of evolution equations in Banach spaces

Josef Kreulich

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We study the asymptotic behavior of solutions to the---generally nonautonomous and nonlinear---Cauchy problem $$ u^{\prime}(t) \in A(t)u(t) + f(t), \ \ t \in \mathbb{R}^+ , \,\,\, u(0) = u_0. \tag {$CP_t$} $$ The emphasis is on almost-periodicity properties of the solution, in particular on weak almost periodicity (in the sense of Eberlein).

Article information

Differential Integral Equations, Volume 9, Number 5 (1996), 1005-1027.

First available in Project Euclid: 6 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34G20: Nonlinear equations [See also 47Hxx, 47Jxx]
Secondary: 34A60: Differential inclusions [See also 49J21, 49K21] 34C27: Almost and pseudo-almost periodic solutions 47H20: Semigroups of nonlinear operators [See also 37L05, 47J35, 54H15, 58D07]


Kreulich, Josef. Eberlein-weakly almost-periodic solutions of evolution equations in Banach spaces. Differential Integral Equations 9 (1996), no. 5, 1005--1027. https://projecteuclid.org/euclid.die/1367871528

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