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.
Aliev, Akbar B., Mamedova, Ulviya M. (2010)
Advances in Difference Equations [electronic only]
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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 can be approximated by a sequence of maximal monotone operators of type NI, which converge to in a reasonable sense (in the sense of Kuratowski-Painleve convergence).
Heikkilä, S., Kumpulainen, M., Lakshmikantham, V. (1992)
Journal of Applied Mathematics and Stochastic Analysis
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Peng, Jian-Wen, Zhao, Lai-Jun (2009)
Journal of Inequalities and Applications [electronic only]
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Jan Franců (1990)
Aplikace matematiky
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The paper deals with the existence of solutions of the form with operators monotone in a broader sense, including pseudomonotone operators and operators satisfying conditions and . 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 . The second part which has a character of a survey compares various...
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.