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Semicontinuity and continuous selections for the multivalued superposition operator without assuming growth-type conditions

Hông Thái Nguyêñ (2004)

Studia Mathematica

Let Ω be a measure space, and E, F be separable Banach spaces. Given a multifunction f : Ω × E 2 F , denote by N f ( x ) the set of all measurable selections of the multifunction f ( · , x ( · ) ) : Ω 2 F , s ↦ f(s,x(s)), for a function x: Ω → E. First, we obtain new theorems on H-upper/H-lower/lower semicontinuity (without assuming any conditions on the growth of the generating multifunction f(s,u) with respect to u) for the multivalued (Nemytskiĭ) superposition operator N f mapping some open domain G ⊂ X into 2 Y , where X and Y are Köthe-Bochner...

Semiflows and semigroups

Edoardo Vesentini (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Given a compact Hausdorff space K and a strongly continuous semigroup T of linear isometries of the Banach space of all complex-valued, continuous functions on K , the semiflow induced by T on K is investigated. In the particular case in which K is a compact, connected, differentiable manifold, a class of semigroups T preserving the differentiable structure of K is characterized.

Semigroup Analysis of Structured Parasite Populations

J. Z. Farkas, D. M. Green, P. Hinow (2010)

Mathematical Modelling of Natural Phenomena

Motivated by structured parasite populations in aquaculture we consider a class of size-structured population models, where individuals may be recruited into the population with distributed states at birth. The mathematical model which describes the evolution of such a population is a first-order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral...

Semigroup approach to the Stefan problem with non-linear flux

Enrico Magenes, Claudio Verdi, Augusto Visintin (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Un problema di Stefan a due fasi con condizione di flusso non lineare sulla parte fissa della frontiera è affrontato mediante la teoria dei semigruppi di contrazione in L 1 . Si dimostra l'esistenza e l’unicità della soluzione nel senso di Crandall-Liggett e Bénilan.

Semigroup commutators under differences (II).

Nicholas Th. Varopoulos (1993)

Revista Matemática Iberoamericana

This is the second instalment of my previous paper with the same title, [1]. This paper consists of two different parts. The first part is devoted to improvements of the results developed in [1]. These improvements are described in section 0.1 below and developed in sections 1 to 5, and 9 to 10; they are in fact technically distinct from [1] and rely on a systematic use of microlocalisation in the context of Hörmander-Weyl calculus. These paragraphs can therefore be read quite independently from...

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