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The paper deals with the properties of a monotone operator defined on a subset of an ordered Banach space. The structure of the set of fixed points between the minimal and maximal ones is described.

Monotone mappings and flows of viscous media.

Klimov, V.S. (2004)

Sibirskij Matematicheskij Zhurnal

Monotone operators. A survey directed to applications to differential equations

Jan Franců (1990)

Aplikace matematiky

The paper deals with the existence of solutions of the form $A u = b$ with operators monotone in a broader sense, including pseudomonotone operators and operators satisfying conditions $S$ and $M$ . The first part of the paper which has a methodical character is concluded by the proof of an existence theorem for the equation on a reflexive separable Banach space with a bounded demicontinuous coercive operator satisfying condition ${(M)}_{0}$ . The second part which has a character of a survey compares various types of...

Monotone operators in divergence form with $x$ -dependent multivalued graphs

Gilles Francfort, François Murat, Luc Tartar (2004)

Bollettino dell'Unione Matematica Italiana

We prove the existence of solutions to $- div a (x, grad u) = f$ , together with appropriate boundary conditions, whenever $a (x, e)$ is a maximal monotone graph in $e$ , for every fixed $x$ . We propose an adequate setting for this problem, in particular as far as measurability is concerned. It consists in looking at the graph after a $45^{\circ}$ rotation, for every fixed $x$ ; in other words, the graph $d \in a (x, e)$ is defined through $d - e = φ (x, d + e)$ , where $φ$ is a Carathéodory contraction in $R^{N}$ . This definition is shown to be equivalent to the fact that $a (x, \cdot)$ is pointwise monotone...

Monotone operators with linear range

Jens Frehse (1983)

Banach Center Publications

Monotonic solutions for quadratic integral equations

Mieczysław Cichoń, Mohamed M.A. Metwali (2011)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Using the Darbo fixed point theorem associated with the measure of noncompactness, we establish the existence of monotonic integrable solution on a half-line ℝ₊ for a nonlinear quadratic functional integral equation.

Monotonic solutions of functional integral and differential equations of fractional order.

El-Sayed, A.M.A., Hashem, H.H.G. (2009)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Morse-Sard theorem for real-analytic functions

Jiří Souček, Vladimír Souček (1972)

Commentationes Mathematicae Universitatis Carolinae

Moudafi's viscosity approximations with demi-continuous and strong pseudo-contractions for non-expansive semigroups.

Wu, Changqun, Cho, Sun Young, Shang, Meijuan (2010)

Journal of Inequalities and Applications [electronic only]

Multiapplications à retraction finie

Jean Jacques Moreau (1974)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Multifunctions of two variables: examples and counterexamples

Jürgen Appell (1996)

Banach Center Publications

A brief account of the connections between Carathéodory multifunctions, Scorza-Dragoni multifunctions, product-measurable multifunctions, and superpositionally measurable multifunctions of two variables is given.

Multilinear almost diagonal estimates and applications

Árpád Bényi, Nikolaos Tzirakis (2004)

Studia Mathematica

We prove that an almost diagonal condition on the (m + 1)-linear tensor associated to an m-linear operator implies boundedness of the operator on products of classical function spaces. We then provide applications to the study of certain singular integral operators.

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