Geodesic
On the Solvability of a Class of Nonlinear Hammerstein--Stieltjes Integral Equations on the Whole Line
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 308 (2020), pp. 253-264

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

We consider a nonlinear integral equation on the whole line with a Hammerstein–Stieltjes integral operator whose pre-kernel is a continuous distribution function. Under certain conditions imposed on the nonlinearity, we prove constructive existence and uniqueness theorems for nonnegative monotone bounded solutions. Some qualitative properties of the constructed solution are also studied. In particular, the results proved in the paper contain a theorem of O. Diekmann as a special case.
Mots-clés : pre-kernel, convergence.
Keywords: iterations, monotonicity, bounded solution 
@article{TM_2020_308_a18,
     author = {Kh. A. Khachatryan and H. S. Petrosyan},
     title = {On the {Solvability} of a {Class} of {Nonlinear} {Hammerstein--Stieltjes} {Integral} {Equations} on the {Whole} {Line}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {253--264},
     publisher = {mathdoc},
     volume = {308},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2020_308_a18/}
}
TY  - JOUR
AU  - Kh. A. Khachatryan
AU  - H. S. Petrosyan
TI  - On the Solvability of a Class of Nonlinear Hammerstein--Stieltjes Integral Equations on the Whole Line
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2020
SP  - 253
EP  - 264
VL  - 308
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2020_308_a18/
LA  - ru
ID  - TM_2020_308_a18
ER  - 
%0 Journal Article
%A Kh. A. Khachatryan
%A H. S. Petrosyan
%T On the Solvability of a Class of Nonlinear Hammerstein--Stieltjes Integral Equations on the Whole Line
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2020
%P 253-264
%V 308
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2020_308_a18/
%G ru
%F TM_2020_308_a18
Kh. A. Khachatryan; H. S. Petrosyan. On the Solvability of a Class of Nonlinear Hammerstein--Stieltjes Integral Equations on the Whole Line. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 308 (2020), pp. 253-264. http://geodesic.mathdoc.fr/item/TM_2020_308_a18/