Monotone operators. A survey directed to applications to differential equations
Aplikace matematiky (1990)
- Volume: 35, Issue: 4, page 257-301
- ISSN: 0862-7940
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topFranců, Jan. "Monotone operators. A survey directed to applications to differential equations." Aplikace matematiky 35.4 (1990): 257-301. <http://eudml.org/doc/15631>.
@article{Franců1990,
abstract = {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.},
author = {Franců, Jan},
journal = {Aplikace matematiky},
keywords = {monotone; pseudomonotone operators; operators satisfying $S$; $M$ conditions; existence theorems for boundary value problems for differential equations; monotone operators; surjectivity of a monotone hemicontinuous coercive operator},
language = {eng},
number = {4},
pages = {257-301},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Monotone operators. A survey directed to applications to differential equations},
url = {http://eudml.org/doc/15631},
volume = {35},
year = {1990},
}
TY - JOUR
AU - Franců, Jan
TI - Monotone operators. A survey directed to applications to differential equations
JO - Aplikace matematiky
PY - 1990
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 35
IS - 4
SP - 257
EP - 301
AB - 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.
LA - eng
KW - monotone; pseudomonotone operators; operators satisfying $S$; $M$ conditions; existence theorems for boundary value problems for differential equations; monotone operators; surjectivity of a monotone hemicontinuous coercive operator
UR - http://eudml.org/doc/15631
ER -
References
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