Geodesic
On the Existence of Solutions for Abstract Nonlinear Operator Equations
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 1089-1100

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We provide a duality theory and existence results for a operator equation $\nabla T(x) = \nabla N(x)$ where $T$ is not necessarily a monotone operator. We use the abstract version of the so called dual variational method. The solution is obtained as a limit of a minimizng sequence whose existence and convergence is proved. 
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     author = {Galewski, Marek},
     title = {On the {Existence} of {Solutions} for {Abstract} {Nonlinear} {Operator} {Equations}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {1089--1100},
     publisher = {mathdoc},
     volume = {Ser. 8, 10B},
     number = {3},
     year = {2007},
     zbl = {1236.47063},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a42/}
}
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Galewski, Marek. On the Existence of Solutions for Abstract Nonlinear Operator Equations. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 1089-1100. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a42/