On total preservation of solvability of controlled Hammerstein-type equation with non-isotone and non-majorizable operator
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We prove some nontrivial corollaries of the Schauder theorem. We use these corollaries to prove a theorem concerning the total preservation of solvability of a controlled functional operator equation of the Hammerstein type with non-isotone and non-majorizable operator component in the right-hand side. We illustrate the application of the abstract theory by the example of the Dirichlet problem associated with a semilinear elliptic equation similar to a stationary diffusionreaction equation.
Keywordsfixed point Hammerstein type equation semilinear elliptic equation of diffusion-reaction type
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- 15.Varga, J. Optimal Control of Differential and Functional Equations (Academic Press, New York, 1972; Nauka, Moscow, 1977).Google Scholar
- 18.Karchevskii, M. M. and Pavlova, M. F. Equations of Mathematical Physics. Additional Chapters (Kazan Univ. Press, Kazan, 2012) [in Russian].Google Scholar
- 19.Vorob’ev, A. Kh. Diffusion Problems in Chemical Kinetics (Moscow Univ. Press, Moscow, 2003) [in Russian].Google Scholar
- 22.Chernov, A. V. “On Total Preservation of Solvability of Controlled Diriclet Problem for Elliptic Equation”, in Proceedings of International Conference dedicated to the 90th Anniversary of Academician N. N. Krasovski ‘Systems Dynamics and Control Processes’ (SDCP’2014) (IMM UrO RAN, Ekateringurg, 2015), pp. 359–366 (2015).Google Scholar