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Displaying similar documents to “Upper Semicontinuous Perturbations of m-accretive Operators and Differential Inclusions with Dissipative Right-hand Side”

On the topological structure of the solution set for a semilinear ffunctional-differential inclusion in a Banach space

Giuseppe Conti, Valeri Obukhovskiĭ, Pietro Zecca (1996)

Banach Center Publications

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In this paper we show that the set of all mild solutions of the Cauchy problem for a functional-differential inclusion in a separable Banach space E of the form x’(t) ∈ A(t)x(t) + F(t,xt) is an R δ -set. Here A(t) is a family of linear operators and F is a Carathéodory type multifunction. We use the existence result proved by V. V. Obukhovskiĭ [22] and extend theorems on the structure of solutions sets obtained by N. S. Papageorgiou [23] and Ya. I. Umanskiĭ [32].

Some remarks on the space of differences of sublinear functions

Sven Bartels, Diethard Pallaschke (1994)

Applicationes Mathematicae

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Two properties concerning the space of differences of sublinear functions D(X) for a real Banach space X are proved. First, we show that for a real separable Banach space (X,‖·‖) there exists a countable family of seminorms such that D(X) becomes a Fréchet space. For X = ℝ^n this construction yields a norm such that D(ℝ^n) becomes a Banach space. Furthermore, we show that for a real Banach space with a smooth dual every sublinear Lipschitzian function can be expressed by the Fenchel...

Second order evolution equations with parameter

Jan Bochenek, Teresa Winiarska (1994)

Annales Polonici Mathematici

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We give some theorems on continuity and differentiability with respect to (h,t) of the solution of a second order evolution problem with parameter h ∈ Ω ⊂ ℝ m . Our main tool is the theory of strongly continuous cosine families of linear operators in Banach spaces.