Geodesic
Increasing Monotone Operators in Banach Space
Matematičeskie zametki, Tome 71 (2002) no. 2, pp. 214-226

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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 $A$. 
@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},
     publisher = {mathdoc},
     volume = {71},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_2_a4/}
}
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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/