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

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Zbl
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. 
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/
@article{BUMI_2007_8_10B_3_a42,
     author = {Galewski, Marek},
     title = {On the {Existence} of {Solutions} for {Abstract} {Nonlinear} {Operator} {Equations}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {1089--1100},
     year = {2007},
     volume = {Ser. 8, 10B},
     number = {3},
     zbl = {1236.47063},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a42/}
}
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