Abstract
In this chapter, we base on Gajewski et al. (Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie-Verlag, Berlin, 1974) and Franců (Aplikace matematiky 35(4), 257–301, 1990) adding some examples and ideas from Drábek and Milota (Methods of nonlinear analysis. Applications to differential equations, 2nd edn, Birkhäuser, Basel, 2013), Denkowski et al. (An introduction to nonlinear analysis: theory, Kluwer, Boston, 2003; An introduction to nonlinear analysis: applications, Kluwer, Boston, 2003), and Migórski and Sofonea (Variational–hemivariational inequalities with applications, Chapman & Hall, Boca Raton, 2018).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
H.H. Bauschke, P.L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces. CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC (Springer, Cham, 2017)
R. Chiappinelli, D.E. Edmunds, Remarks on Surjectivity of Gradient operators. Mathematics 8, 1538 (2020). https://doi.org/10.3390/math8091538
Z. Denkowski, S. Migórski, N.S. Papageorgiou, An Introduction to Nonlinear Analysis: Theory (Kluwer Academic/Plenum Publishers, New York, 2003)
Z. Denkowski, S. Migórski, N.S. Papageorgiou, An Introduction to Nonlinear Analysis: Applications (Kluwer Academic/Plenum Publishers, New York, 2003)
P. Drábek, J. Milota, Methods of Nonlinear Analysis. Applications to Differential Equations, 2nd edn. Birkhäuser Advanced Texts. Basler Lehrbücher (Springer, Basel, 2013)
J. Franců, Monotone operators: a survey directed to applications to differential equations. Aplikace Matematiky 35(4), 257–301 (1990)
H. Gajewski, K. Gröger, K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen (Akademie, Berlin, 1974)
R.I. Kačurovskiı̆, Monotone operators and convex functionals. Uspekhi Mat. Nauk 15, 213–215 (1960)
R.I. Kačurovskiı̆, Nonlinear monotone operators in Banach spaces. Uspekhi Mat. Nauk 23, 121–168 (1968); English translation: Russian Math. Surveys 23, 117–165 (1968)
S. Migórski, M. Sofonea, Variational–Hemivariational inequalities with applications, in Chapman & Hall/CRC Monographs and Research Notes in Mathematics, Boca Raton, FL (2018)
G.J. Minty, Monotone (nonlinear) operators in Hilbert space. Duke Math. J. 29, 341–346 (1962)
G.J. Minty, On a “monotonicity” method for the solution of nonlinear equations in Banach spaces. Proc. Natl. Acad. Sci. USA 50, 1038–1041 (1963)
W. Rudin, Functional analysis, in McGraw-Hill Series in Higher Mathematics (McGraw-Hill Book Co., New York, 1973)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Galewski, M. (2021). Monotone Operators. In: Basic Monotonicity Methods with Some Applications. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-75308-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-75308-5_3
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-75307-8
Online ISBN: 978-3-030-75308-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)