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Russian Mathematics

, Volume 61, Issue 6, pp 72–81 | Cite as

On total preservation of solvability of controlled Hammerstein-type equation with non-isotone and non-majorizable operator

  • A. V. ChernovEmail author
Article
  • 19 Downloads

Abstract

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.

Keywords

fixed point Hammerstein type equation semilinear elliptic equation of diffusion-reaction type 

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© Allerton Press, Inc. 2017

Authors and Affiliations

  1. 1.Nizhny Novgorod State University named after N. I. LobachevskiiNizhny NovgorodRussia
  2. 2.Nizhny Novgorod State Technical University named after R. E. AlekseevNizhny NovgorodRussia

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