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Monotone operators. A survey directed to applications to differential equations
Applications of Mathematics, Tome 35 (1990) no. 4, pp. 257-301
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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.
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.
DOI : 10.21136/AM.1990.104411
Classification : 35-02, 35A05, 35A25, 35F30, 47H05, 47H15, 65J15
Keywords: monotone; pseudomonotone operators; operators satisfying $S$, $M$ conditions; existence theorems for boundary value problems for differential equations 
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Franců, Jan. Monotone operators. A survey directed to applications to differential equations. Applications of Mathematics, Tome 35 (1990) no. 4, pp. 257-301. doi: 10.21136/AM.1990.104411

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