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Uniformly bounded Nemytskij operators acting between the Banach spaces of generalized Hölder functions [PDF]
Journal of Applied Mathematics and Computational Mechanics, 2017 Maria Lupa, Małgorzata Wróbel
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Finite Element Approximation of Lyapunov Equations Related to Parabolic Stochastic PDEs. [PDF]
Appl Math OptimAndersson A +3 more
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Upper semicontinuity of Nemytskij operators
Annali di Matematica Pura ed Applicata, 1991The authors give a growth condition on a multivalued nonlinear function \(G=G(\lambda,u)\), under which the upper semicontinuity of the function \(G(\lambda,\cdot)\) implies the upper semicontinuity of the multivalued Nemytskij operator generated by \(G\) between two Lebesgue-Bochner spaces. Similar results have been given by the reviewer, \textit{H. T.
CELLINA, ARRIGO +2 more
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The autonomous Nemytskij operator in Hölder spaces
Nonlinear Analysis: Theory, Methods & Applications, 1997The author gives a survey on acting, continuity, Lipschitz, and differentiability conditions of the Nemytskij operator \(Fx= f\circ x\), in terms of the generating nonlinear function \(f\), in the Hölder spaces \(H^\alpha[a, b]\) and \(H^{k+\alpha}[a, b]\) (\(k\in\mathbb{N ...
Goebel, Manfred, Sachweh, Frank
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Hyperbolic equations, function spaces with exponential weights and Nemytskij operators
Annali di Matematica Pura ed Applicata, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bourdaud, Gérard +2 more
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Zeitschrift für Analysis und ihre Anwendungen, 2002
We consider systems of quasilinear partial differential equations of second order in two- and three-dimensional domains with corners and edges. The analysis is performed in weighted Sobolev spaces with attached asymptotics generated by the asymptotic behaviour of the solutions of the corresponding linearized problems near boundary singularities ...
Ali Mehmeti, F. +3 more
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We consider systems of quasilinear partial differential equations of second order in two- and three-dimensional domains with corners and edges. The analysis is performed in weighted Sobolev spaces with attached asymptotics generated by the asymptotic behaviour of the solutions of the corresponding linearized problems near boundary singularities ...
Ali Mehmeti, F. +3 more
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On N
AbstractThis paper is concerned with continuity and differentiability of NEMYTSKIJ operators acting between spaces of summable abstract functions. In a first part, necessary and sufficient conditions for continuity are collected. Then main emphasis is given to sufficient conditions for differentiability in the sense of FRÉCHET and GÂTEAUX.
Goldberg, H. +2 more
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On Nemytskii operator for set-valued functions
Publicationes Mathematicae Debrecen, 1999The author presents generalizations (in some sense) of her previous results that appeared in [Publ. Math. 54, No. 1-2, 33-37 (1999; Zbl 0921.47056)]. In fact, here she treats the problem of characterizing those vector-valued, or set-valued functions that generate such a Nemytskij operator which maps a \(\text{lip}^2\) space (space of functions with ...
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On Nemytskij operator in the space of absolutely continuous set-valued functions
Journal of Applied Analysis, 2011Summary: We consider the Nemytskij operator, defined by \((N\phi)(x) := G(x, \phi(x))\), where \(G\) is a given set-valued function. It is shown that if \(N\) maps \(AC(I, C)\), the space of all absolutely continuous functions on the interval \(I := [0, 1]\) with values in a cone \(C\) in a reflexive Banach space, into \(AC(I, \mathcal K)\), the space ...
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