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Note on Perturbation and Degeneration of Abstract Differential Equations in Banach Space

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Differential equations in spaces of abstract stochastic distributions

Doklady Mathematics, 2016
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Melnikova, Irina V., Alshanskiy, M. A.
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Differential equations in spaces of abstract stochastic distributions

Stochastics and Stochastic Reports, 2002
We develop the theory of stochastic distributions with values in a separable Hilbert space, and apply this theory to the investigation of abstract stochastic evolution equations with additive noise.
Filinkov, A., Sorensen, J.
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Existence of Solutions of Abstract Differential Equations in a Local Space

Canadian Mathematical Bulletin, 1973
Let H be a Hilbert space; ( , ) and | | represent the scalar product and the norm respectively in H. Let A be a closed linear operator with domain DA dense in H and A* be its adjoint with domain DA*. DA and DA*are also Hilbert spaces under their respective graph scalar product. R(λ; A*) denotes the resolvent of A*; complex plane. We write L = D — A, L*
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Differential equations in abstract spaces

1997
In this chapter, we are concerned with the initial value problem: $$\left\{ {\begin{array}{*{20}{c}} {y'\left( t \right) = f\left( {t,y\left( t \right)} \right){\text{ }}t \in \left[ {0,T} \right]} \\ {y\left( 0 \right) = a \in E;} \end{array}} \right.$$ (1.1) where E is a real Banach space and f : [0, T] × E → E has a decomposition f = g + h
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