Geodesic
A majorant-minorant criterion for the total preservation of global solvability of a~functional operator equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2012), pp. 62-73

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We study a nonlinear controlled functional operator equation in an ideal Banach space. We establish sufficient conditions for the global solvability for all controls from a given set, and obtain a pointwise estimate for solutions. Using upper and lower estimates of the functional component in the right-hand side of the initial equation (with a fixed operator component), we obtain majorant and minorant equations.We prove the stated theorem, assuming the monotonicity of the operator component in the right-hand side and the global solvability of both majorant and minorant equations. We give examples of the reduction of controlled initial boundary value problems to the equation under consideration.
Keywords: total preservation of global solvability, functional operator equation, pointwise estimate of solutions. 
@article{IVM_2012_3_a7,
     author = {A. V. Chernov},
     title = {A majorant-minorant criterion for the total preservation of global solvability of a~functional operator equation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {62--73},
     publisher = {mathdoc},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_3_a7/}
}
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A. V. Chernov. A majorant-minorant criterion for the total preservation of global solvability of a~functional operator equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2012), pp. 62-73. http://geodesic.mathdoc.fr/item/IVM_2012_3_a7/