Geodesic
Increasing Monotone Operators in Banach Space
Matematičeskie zametki, Tome 71 (2002) no. 2, pp. 214-226 
G. I. Laptev. Increasing Monotone Operators in Banach Space. Matematičeskie zametki, Tome 71 (2002) no. 2, pp. 214-226. http://geodesic.mathdoc.fr/item/MZM_2002_71_2_a4/
@article{MZM_2002_71_2_a4,
     author = {G. I. Laptev},
     title = {Increasing {Monotone} {Operators} in {Banach} {Space}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {214--226},
     year = {2002},
     volume = {71},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_2_a4/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

An operator $A$ mapping a separable reflexive Banach space $X$ into the dual space $X'$ is called increasing if $\|Au\|\to \infty$ as $\|u\|\to \infty$. Necessary and sufficient conditions for the superposition operators to be increasing are obtained. The relationship between the increasing and coercive properties of monotone partial differential operators is studied. Additional conditions are imposed that imply the existence of a solution for the equation $Au=f$ with an increasing operator $A$.

[1] Gaevskii Kh., Greger K., Zakharias K., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Nauka, M., 1978

[2] Lions Zh.-L., Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972

[3] Dubinskii Yu. A., “Nelineinye ellipticheskie i parabolicheskie uravneniya”, Itogi nauki i tekhniki. Sovremennye problemy matematiki, 9, VINITI, M., 1976, 5–130

[4] Skrypnik I. V., Metody issledovaniya nelineinykh ellipticheskikh granichnykh zadach, Nauka, M., 1990

[5] Miloevich P. S., “Razreshimost silno nelineinykh operatornykh uravnenii i ikh prilozheniya”, Differents. uravneniya, 31:3 (1995), 502–516 | MR

[6] Krasnoselskii M. A., Topologicheskie metody v teorii nelineinykh integralnykh uravnenii, Gostekhizdat, M., 1956

[7] Nirenberg L., Lektsii po nelineinomu funktsionalnomu analizu, Mir, M., 1977 | Zbl

[8] Pokhozhaev S. I., “O razreshimosti nelineinykh uravnenii s nechetnymi operatorami”, Funktsion. analiz i ego prilozh., 1:3 (1967), 66–73 | MR | Zbl