| Title:
|
Monotone operators. A survey directed to applications to differential equations (English) |
| Author:
|
Franců, Jan |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
35 |
| Issue:
|
4 |
| Year:
|
1990 |
| Pages:
|
257-301 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
monotone |
| Keyword:
|
pseudomonotone operators |
| Keyword:
|
operators satisfying $S$, $M$ conditions |
| Keyword:
|
existence theorems for boundary value problems for differential equations |
| MSC:
|
35-02 |
| MSC:
|
35A05 |
| MSC:
|
35A25 |
| MSC:
|
35F30 |
| MSC:
|
47H05 |
| MSC:
|
47H15 |
| MSC:
|
65J15 |
| idZBL:
|
Zbl 0724.47025 |
| idMR:
|
MR1065003 |
| DOI:
|
10.21136/AM.1990.104411 |
| . |
| Date available:
|
2008-05-20T18:39:31Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104411 |
| . |
| Reference:
|
[1] K. Deimling: Nonlinear functional analysis.Springer 1985. Zbl 0559.47040, MR 0787404 |
| Reference:
|
[2] P. Doktor: Modern methods of solving partial differential equations.(Czech), Lecture Notes, SPN, Prague, 1976. |
| Reference:
|
[3] S. Fučík: Solvability of nonlinear equations and boundary value problems.D. Reidel Publ. Соmр., Dordrecht; JČSMF, Prague, 1980. MR 0620638 |
| Reference:
|
[4] S. Fučík A. Kufner: Nonlinear differential equations;.Czech edition - SNTL, Prague 1978; English translation - Elsevier, Amsterdam 1980. MR 0558764 |
| Reference:
|
[5] S. Fučík J. Milota: Mathematical analysis II.(Czech), Lecture Notes, SPN, Prague 1980. |
| Reference:
|
[6] S. Fučík J. Nečas J. Souček V. Souček: Spectral analysis of nonlinear operators.Lecture Notes in Math. 346, Springer, Berlin 1973; JCSMF, Prague 1973. MR 0467421 |
| Reference:
|
[7] R. I. Kačurovskij: Nonlinear monotone operators in Banach spaces.(Russian), Uspechi Mat. Nauk 23 (1968), 2, 121-168. MR 0226455 |
| Reference:
|
[8] D. Kinderlehrer G. Stampacchia: An introduction to variational inequalities and their applications.Academic Press, New York 1980; Russian translation - Mir, Moscow 1983. MR 0738631 |
| Reference:
|
[9] A. N. Kolmogorov S. V. Fomin: Introductory real analysis.(Russian), Moscow 1954, English translation - Prentice Hall, New York 1970, Czech translation - SNTL, Prague 1975. MR 0267052 |
| Reference:
|
[10] A. Kufner O. John S. Fučík: Function spaces.Academia, Prague 1977. MR 0482102 |
| Reference:
|
[11] J. Nečas: Introduction to the theory of nonlinear elliptic equations.Teubner-Texte zur Math. 52, Leipzig, 1983. MR 0731261 |
| Reference:
|
[12] D. Pascali S. Sburlan: Nonlinear mappings of monotone type.Editura Academiei, Bucuresti 1978. MR 0531036 |
| Reference:
|
[13] A. Pultr: Subspaces of Euclidean spaces.(Czech), Matematický seminář - 22, SNTL, Prague 1987. |
| Reference:
|
[14] 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). MR 0628004 |
| Reference:
|
[15] J. Nečas: Nonlinear elliptic equations.(French), Czech. Math. J. 19 (1969), 252-274. |
| Reference:
|
[16] M. Feistauer A. Ženíšek: Compactness method in the finite element theory of nonlinear elliptic problems.Numer. Math. 52 (1988), 147-163. MR 0923708, 10.1007/BF01398687 |
| . |
