Monotone operators. A survey directed to applications to differential equations
Franců, Jan
Applications of Mathematics, Tome 35 (1990), p. 257-301 / Harvested from Czech Digital Mathematics Library
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The paper deals with the existence of solutions of the form $Au=b$ 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 continuity and monotony and introduces further results. Application of this theory to proofs of existence theorems for boundary value problems for ordinary and partial differential equations is illustrated by examples.

Publié le : 1990-01-01
Classification:  35-02,  35A05,  35A25,  35F30,  47H05,  47H15,  65J15 
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     author = {Jan Franc\r u},
     title = {Monotone operators. A survey directed to applications to differential equations},
     journal = {Applications of Mathematics},
     volume = {35},
     year = {1990},
     pages = {257-301},
     zbl = {0724.47025},
     mrnumber = {1065003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104411}
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Franců, Jan. Monotone operators. A survey directed to applications to differential equations. Applications of Mathematics, Tome 35 (1990) pp. 257-301. http://gdmltest.u-ga.fr/item/104411/

K. Deimling Nonlinear functional analysis, Springer 1985. (1985) | MR 0787404 | Zbl 0559.47040

P. Doktor Modern methods of solving partial differential equations, (Czech), Lecture Notes, SPN, Prague, 1976. (1976)

S. Fučík Solvability of nonlinear equations and boundary value problems, D. Reidel Publ. Соmр., Dordrecht; JČSMF, Prague, 1980. (1980) | MR 0620638

S. Fučík A. Kufner Nonlinear differential equations;, Czech edition - SNTL, Prague 1978; English translation - Elsevier, Amsterdam 1980. (1978) | MR 0558764

S. Fučík J. Milota Mathematical analysis II, (Czech), Lecture Notes, SPN, Prague 1980. (1980)

S. Fučík J. Nečas J. Souček V. Souček Spectral analysis of nonlinear operators, Lecture Notes in Math. 346, Springer, Berlin 1973; JCSMF, Prague 1973. (1973) | MR 0467421

R. I. Kačurovskij Nonlinear monotone operators in Banach spaces, (Russian), Uspechi Mat. Nauk 23 (1968), 2, 121-168. (1968) | MR 0226455

D. Kinderlehrer G. Stampacchia An introduction to variational inequalities and their applications, Academic Press, New York 1980; Russian translation - Mir, Moscow 1983. (1980) | MR 0738631

A. N. Kolmogorov S. V. Fomin Introductory real analysis, (Russian), Moscow 1954, English translation - Prentice Hall, New York 1970, Czech translation - SNTL, Prague 1975. (1954) | MR 0267052

A. Kufner O. John S. Fučík Function spaces, Academia, Prague 1977. (1977) | MR 0482102

J. Nečas Introduction to the theory of nonlinear elliptic equations, Teubner-Texte zur Math. 52, Leipzig, 1983. (1983) | MR 0731261

D. Pascali S. Sburlan Nonlinear mappings of monotone type, Editura Academiei, Bucuresti 1978. (1978) | MR 0531036

A. Pultr Subspaces of Euclidean spaces, (Czech), Matematický seminář - 22, SNTL, Prague 1987. (1987)

E. Zeidler Lectures on nonlinear functional analysis II - Monotone operators, (German), Teubner-Texte zur Math. 9, Leipzig 1977; Revised extended English translation: Nonlinear functional analysis and its application II, Springer, New York (to appear). (1977) | MR 0628004

J. Nečas Nonlinear elliptic equations, (French), Czech. Math. J. 19 (1969), 252-274. (1969)

M. Feistauer A. Ženíšek Compactness method in the finite element theory of nonlinear elliptic problems, Numer. Math. 52 (1988), 147-163. (1988) | Article | MR 0923708