On a generalization of the method of monotone operators |
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Authors: | A V Chernov |
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Institution: | 1. Nizhni Novgorod State Technical University, Nizhni Novgorod, Russia 2. Nizhni Novgorod State University, Nizhni Novgorod, Russia
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Abstract: | For a family of operator equations of the first kind with nonlinear nonmonotone hemicontinuous operators in a reflexive Banach space, we prove a theorem on the solvability and a uniform estimate of the solution in the norm of the space. Our approach is related to the method of semimonotone operators but has some essential differences from the latter. In a specific example, we show that our theorem can be used to prove the total (with respect to the set of admissible controls) preservation of solvability for distributed control systems. |
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