On the mild solutions of higher-order differential equations in Banach spaces
نویسندگان
چکیده
منابع مشابه
On the Mild Solutions of Higher-order Differential Equations in Banach Spaces
For the higher-order abstract differential equation u(n)(t) = Au(t) + f (t), t ∈ R, we give a new definition of mild solutions. We then characterize the regular admissibility of a translation-invariant subspace of BUC(R,E) with respect to the above-mentioned equation in terms of solvability of the operator equation AX −X n = C. As applications, periodicity and almost periodicity of mild solutio...
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For the complete higher order differential equation u(t) = Σn−1 k=0Aku (t) + f(t), t ∈ R (*) on a Banach space E, we give a new definition of mild solutions of (*). We then characterize the regular admissibility of a translation invariant subspace M of BUC(R,E) with respect to (*) in terms of solvability of the operator equation Σn−1 j=0AjXD j −XD = C. As application, almost periodicity of mild...
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For the complete higher order differential equation
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We study the existence of mild solutions for semilinear fractional differential equations with nonlocal initial conditions in $L^p([0,1],E)$, where $E$ is a separable Banach space. The main ingredients used in the proof of our results are measure of noncompactness, Darbo and Schauder fixed point theorems. Finally, an application is proved to illustrate the results of this work.
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where Aj are linear, closed operators on a Banach space E and f is a function from [0, T ] to E. The asymptotic behavior and, in particular, the periodicity of solutions of the higher order differential equation u(t) = Au(t) + f(t), 0 ≤ t ≤ T, (1.2) has been an subject of intensive study for recent decades. When n = 1, it is well-known [7] that, if A is an n×n matrix on C, then (1.2) admits a u...
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ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2003
ISSN: 1085-3375,1687-0409
DOI: 10.1155/s1085337503303057