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Applicable Analysis
An International Journal
Volume 5, 1975 - Issue 2
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Original Articles

Flow-invariant sets and differential inequalities in normed spacesFootnote†

R. M. Redheffer Mathematisches Institut I, Universitat Karlsruhe (TH), Postfach, Karlsruhe, 6380, Germany
&
W. Walter Mathematisches Institut I, Universitat Karlsruhe (TH), Postfach, Karlsruhe, 6380, Germany
Pages 149-161 | Published online: 02 May 2007

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Qing Hui. (2011) Quantised near-consensus via quantised communication links. International Journal of Control 84:5, pages 931-946.
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Gerd Herzog & Roland Lemmert. (1999) Intermediate value theorems for quasimonotone increasing mappings. Numerical Functional Analysis and Optimization 20:9-10, pages 901-908.
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Thomas C. Gard & V. Lakshmikantham. (1980) Strongly flow-invariant sets. Applicable Analysis 10:4, pages 285-293.
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Haijing Wang, Jinzhu Peng, Juanjuan Xu, Fangfang Zhang & Yaonan Wang. (2023) High‐order control barrier functions‐based optimization control for time‐varying nonlinear systems with full‐state constraints: A dynamic sub‐safe set approach. International Journal of Robust and Nonlinear Control 33:8, pages 4490-4503.
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Guglielmo Feltrin & Fabio Zanolin. (2022) Equilibrium points, periodic solutions and the Brouwer fixed point theorem for convex and non-convex domains. Journal of Fixed Point Theory and Applications 24:4.
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Pedro Gajardo & Alberto Seeger. (2021) Cross-nonnegativity and monotonicity analysis of nonlinear dynamical systems. Journal of Differential Equations 300, pages 33-52.
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Rohit Konda, Aaron D. Ames & Samuel Coogan. (2021) Characterizing Safety: Minimal Control Barrier Functions From Scalar Comparison Systems. IEEE Control Systems Letters 5:2, pages 523-528.
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Pierre Magal, Ousmane Seydi & Feng-Bin Wang. (2021) Positively invariant subset for non-densely defined Cauchy problems. Journal of Mathematical Analysis and Applications 494:2, pages 124600.
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Hannelore Lisei, Csaba Varga & Orsolya Vas. (2018) Localization method for the solutions of nonhomogeneous operator equations. Applied Mathematics and Computation 329, pages 64-83.
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Moufida Amiour & Mustapha Fateh Yarou. (2018) Invariant Systems with Dissipative Operators. Bulletin of the Iranian Mathematical Society 44:3, pages 643-657.
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Stéphane Gaubert & Zheng Qu. (2014) The contraction rate in Thompson's part metric of order-preserving flows on a cone – Application to generalized Riccati equations. Journal of Differential Equations 256:8, pages 2902-2948.
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Norma L. Ortiz-Robinson & Vinicio R. Ríos. (2012) Forward Euler Solutions and Weakly Invariant Time-Delayed Systems. Abstract and Applied Analysis 2012, pages 1-15.
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T. Donchev, V. Ríos & P. Wolenski. (2005) Strong invariance and one-sided Lipschitz multifunctions. Nonlinear Analysis: Theory, Methods & Applications 60:5, pages 849-862.
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D. Angeli & E.D. Sontag. (2003) Monotone control systems. IEEE Transactions on Automatic Control 48:10, pages 1684-1698.
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Roland Uhl. (2003) Smallest and greatest fixed points of quasimonotone increasing mappings. Mathematische Nachrichten 248-249:1, pages 204-210.
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Daniel Biles & Eric Schechter. (2000) Solvability of a finite or infinite system of discontinuous quasimonotone differential equations. Proceedings of the American Mathematical Society 128:11, pages 3349-3360.
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Ray Redheffer & Wolfgang Walter. (1986) Remarks on ordinary differential equations in ordered Banach spaces. Monatshefte f�r Mathematik 102:3, pages 237-249.
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Peter Volkmann. (1985) Ein Invarianz-Satz f�r gew�hnliche und parabolische Differentialgleichungen. Archiv der Mathematik 45:2, pages 150-157.
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T. C. Gard. 1984. Mathematical Ecology. Mathematical Ecology 208 219 .
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Wolfgang Walter. (1979) Fixpunkte der Poincar�-Abbildung. Archiv der Mathematik 33:1, pages 80-84.
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J Eisenfeld & V Lakshmikantham. (1979) Differential inequalities and flow-invariance via linear functionals. Journal of Mathematical Analysis and Applications 69:1, pages 104-114.
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Robert H MartinJr.Jr.. (1978) Asymptotic stability and critical points for nonlinear quasimonotone parabolic systems. Journal of Differential Equations 30:3, pages 391-423.
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Roland Lemmert. (1978) Unter- und Oberfunktionen und Differentialungleichungen zweiter Ordnung in normierten Räumen. Proceedings of the American Mathematical Society 70:2, pages 173-180.
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Russell C. Thompson. (1977) An Invariance Property of Solutions to Second Order Differential Inequalities in Ordered Banach Spaces. SIAM Journal on Mathematical Analysis 8:4, pages 592-603.
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V. Lakshmikantham. 1977. Nonlinear Systems and Applications. Nonlinear Systems and Applications 219 230 .
Ray Redheffer & Wolfgang Walter. (1977) Invariant sets for systems of partial differential equations I. Parabolic equations. Archive for Rational Mechanics and Analysis 67:1, pages 41-52.
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Klaus Schmitt & Peter Volkmann. (1976) Boundary value problems for second order differential equations in convex subsets of a Banach space. Transactions of the American Mathematical Society 218:0, pages 397-405.
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Robert H. Martin. (1975) Remarks on differential inequalities in Banach spaces. Proceedings of the American Mathematical Society 53:1, pages 65-71.
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Ray Redheffer. (1975) Matrix differential equations. Bulletin of the American Mathematical Society 81:2, pages 485-488.
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