Results 1 to 10 of about 57 (53)
Quantitative functional calculus in Sobolev spaces
Journal of Function Spaces and Applications, 2004 In the frame work of Sobolev (Bessel potential) spaces Hn(Rd,R or C), we consider the nonlinear Nemytskij operator sending a function x∈Rd↦f(x) into a composite function x∈Rd↦G(f(x),x).
Carlo Morosi, Livio Pizzocchero
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Uniformly bounded set-valued Nemytskij operators acting between generalized Hölder function spaces
Open Mathematics, 2012 Abstract We show that the generator of any uniformly bounded set-valued Nemytskij composition operator acting between generalized Hölder function metric spaces, with nonempty, bounded, closed, and convex values, is an affine function.
Matkowski Janusz, Wróbel Małgorzata
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On Fréchet-differentiability of Nemytskij operators acting in Hölder spaces [PDF]
Glasgow Mathematical Journal, 1991 In any field of nonlinear analysis Nemytskij operators, the superposition operators generated by appropriate functions, play a crucial part. Their analytic properties depend on the postulated properties of the defining function and on the function space in which they are considered. A rich source for related questions is the monograph by J.
Mehmeti Feli Ali, Serge Nicaise
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Mathematical Methods in the Applied Sciences, Volume 44, Issue 17, Page 12860-12880, 30 November 2021., 2021 In this paper, we investigate the numerical approximation of stochastic convection–reaction–diffusion equations using two explicit exponential integrators. The stochastic partial differential equation (SPDE) is driven by additive Wiener process. The approximation in space is done via a combination of the standard finite element method and the Galerkin ...
Antoine Tambue, Jean Daniel Mukam
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Uniformly continuous set-valued composition operators in the space of total φ-bidimensional variation in the sense of Riesz [PDF]
Opuscula Mathematica, 2010 In this paper we prove that if a Nemytskij composition operator, generated by a function of three variables in which the third variable is a function one, maps a suitable large subset of the space of functions of bounded total \(\varphi\)-bidimensional ...
Wadie Aziz +3 more
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On the Autonomous Nemytskij Operator in Hölder Spaces
Zeitschrift für Analysis und ihre Anwendungen, 1999 The paper is devoted to the autonomous Nemytskij operator (superposition operator) in Hölder spaces H^{k+\alpha}[a,b], (k, \alpha) \in \mathbb Z_+ \times [0, 1]. We study acting, continuity, Lipschitz continuity, and Fréchet differentiability conditions. For
Goebel, M., Sachweh, F.
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On uniformly continuous Nemytskij operators generated by set-valued functions [PDF]
Aequationes mathematicae, 2010 The properties of superposition operators generated by set-valued functions are studied. The main result is the following. Theorem. Let \(I = [0, 1]\) and \(Y\) be a real normed linear space, \(Z\) be a Banach space and let \(C\) be a convex cone in \(Y\). Assume that \(\gamma: [0, \infty) \rightarrow [0, \infty)\) is continuous at \(0\), \(\gamma(0) =
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Journal of Function Spaces, Volume 2018, Issue 1, 2018., 2018 We prove the existence of extremal solutions of the following quasilinear elliptic problem -∑i=1N∂/∂xiai(x,u(x),Du(x))+g(x,u(x),Du(x))=0 under Dirichlet boundary condition in Orlicz‐Sobolev spaces W01LM(Ω) and give the enclosure of solutions. The differential part is driven by a Leray‐Lions operator in Orlicz‐Sobolev spaces, while the nonlinear term g ...
Ge Dong, Xiaochun Fang, Alberto Fiorenza
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Locally Lipschitz Composition Operators in Space of the Functions of Bounded κΦ‐Variation
Journal of Function Spaces, Volume 2014, Issue 1, 2014., 2014 We give a necessary and sufficient condition on a function h:R→R under which the nonlinear composition operator H, associated with the function h, Hu(t) = h(u(t)), acts in the space κΦBV[a, b] and satisfies a local Lipschitz condition.
Odalis Mejía +3 more
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Application of Spectral Methods to Boundary Value Problems for Differential Equations
International Scholarly Research Notices, Volume 2011, Issue 1, 2011., 2011 We try to generalize the concept of a spectrum in the nonlinear case starting from its splitting into several subspectra, not necessarily disjoint, following the classical decomposition of the spectrum. To obtain an extension of spectrum with rich properties, we replace the identity map by a nonlinear operator J acting between two Banach spaces X and Y,
Ene Petronela, G. Mantica
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