Finite difference schemes with monotone operators.

Apreutesei, N.C.

Displaying similar documents to “Finite difference schemes with monotone operators.”

Second order difference inclusions of monotone type

G. Apreutesei, N. Apreutesei (2012)

Mathematica Bohemica

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The existence of anti-periodic solutions is studied for a second order difference inclusion associated with a maximal monotone operator in Hilbert spaces. It is the discrete analogue of a well-studied class of differential equations.

A mixed problem for quasilinear impulsive hyperbolic equations with non stationary boundary and transmission conditions.

Aliev, Akbar B., Mamedova, Ulviya M. (2010)

Advances in Difference Equations [electronic only]

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On maximal monotone operators with relatively compact range

Dariusz Zagrodny (2010)

Czechoslovak Mathematical Journal

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It is shown that every maximal monotone operator on a real Banach space with relatively compact range is of type NI. Moreover, if the space has a separable dual space then every maximally monotone operator $T$ can be approximated by a sequence of maximal monotone operators of type NI, which converge to $T$ in a reasonable sense (in the sense of Kuratowski-Painleve convergence).

On solvability of mixed monotone operator equations with applications to mixed quasimonotone differential systems involving discontinuities.

Heikkilä, S., Kumpulainen, M., Lakshmikantham, V. (1992)

Journal of Applied Mathematics and Stochastic Analysis

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General system of $A$ -monotone nonlinear variational inclusions problems with applications.

Peng, Jian-Wen, Zhao, Lai-Jun (2009)

Journal of Inequalities and Applications [electronic only]

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Monotone operators. A survey directed to applications to differential equations

Jan Franců (1990)

Aplikace matematiky

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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...

An existence result for nonlinear evolution equations of second order

Dimitrios A. Kandilakis (1996)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper we consider a second order differential equation involving the difference of two monotone operators. Using an auxiliary equation, a priori bounds and a compactness argument we show that the differential equation has a local solution. An example is also presented in detail.

The solvability of a new system of nonlinear variational-like inclusions.

Liu, Zeqing, Liu, Min, Ume, Jeong Sheok, Kang, Shin Min (2009)

Fixed Point Theory and Applications [electronic only]

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Periodic solutions for quasilinear vector differential equations with maximal monotone terms

Nikolaos C. Kourogenis, Nikolaos S. Papageorgiou (1997)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We consider a quasilinear vector differential equation with maximal monotone term and periodic boundary conditions. Approximating the maximal monotone operator with its Yosida approximation, we introduce an auxiliary problem which we solve using techniques from the theory of nonlinear monotone operators and the Leray-Schauder principle. To obtain a solution of the original problem we pass to the limit as the parameter λ > 0 of the Yosida approximation tends to zero.