Geodesic
On total preservation of solvability for a controlled Hammerstein type equation with non-isotone and non-majorized operator
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2017), pp. 83-94

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove some nontrivial corollaries of the Schauder theorem. We use these corollaries to prove a theorem concerning the total preservation of solvability for a controlled functional operator equation of the Hammerstein type with non-isotone and non-majorized operator component of the right-hand side. We illustrate an application of the abstract theory by the example of the Dirichlet problem associated with a semilinear elliptic equation of the stationary diffusion-reaction type.
Keywords: fixed point, equation of the Hammerstein type, semilinear elliptic equation of the diffusion-reaction type. 
@article{IVM_2017_6_a9,
     author = {A. V. Chernov},
     title = {On total preservation of solvability for a controlled {Hammerstein} type equation with non-isotone and non-majorized operator},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {83--94},
     publisher = {mathdoc},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_6_a9/}
}
TY  - JOUR
AU  - A. V. Chernov
TI  - On total preservation of solvability for a controlled Hammerstein type equation with non-isotone and non-majorized operator
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2017
SP  - 83
EP  - 94
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2017_6_a9/
LA  - ru
ID  - IVM_2017_6_a9
ER  - 
%0 Journal Article
%A A. V. Chernov
%T On total preservation of solvability for a controlled Hammerstein type equation with non-isotone and non-majorized operator
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2017
%P 83-94
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2017_6_a9/
%G ru
%F IVM_2017_6_a9
A. V. Chernov. On total preservation of solvability for a controlled Hammerstein type equation with non-isotone and non-majorized operator. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2017), pp. 83-94. http://geodesic.mathdoc.fr/item/IVM_2017_6_a9/