Geodesic
On nonlinear convolution-type integral equations in the~theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 1, pp. 184-200

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

We study a class of integral equations of convolution type on the whole line with a monotone and odd nonlinearity. We prove constructive existence and absence theorems for nonnegative (nontrivial) and bounded solutions. We study the asymptotic behavior of the constructed solution at $\pm\infty$. We also prove the uniqueness of the solution in the class of nonnegative (nonzero) and bounded functions and present specific examples of this class of equations that can be applied in various fields of mathematical physics.
Keywords: monotonicity, nonlinearity, convexity
Mots-clés : kernel, nonnegative solution, convolution. 
@article{TMF_2023_216_1_a11,
     author = {A. Kh. Khachatryan and Kh. A. Khachatryan and H. S. Petrosyan},
     title = {On nonlinear convolution-type integral equations in the~theory},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {184--200},
     publisher = {mathdoc},
     volume = {216},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_216_1_a11/}
}
TY  - JOUR
AU  - A. Kh. Khachatryan
AU  - Kh. A. Khachatryan
AU  - H. S. Petrosyan
TI  - On nonlinear convolution-type integral equations in the~theory
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2023
SP  - 184
EP  - 200
VL  - 216
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2023_216_1_a11/
LA  - ru
ID  - TMF_2023_216_1_a11
ER  - 
%0 Journal Article
%A A. Kh. Khachatryan
%A Kh. A. Khachatryan
%A H. S. Petrosyan
%T On nonlinear convolution-type integral equations in the~theory
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2023
%P 184-200
%V 216
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2023_216_1_a11/
%G ru
%F TMF_2023_216_1_a11
A. Kh. Khachatryan; Kh. A. Khachatryan; H. S. Petrosyan. On nonlinear convolution-type integral equations in the~theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 1, pp. 184-200. http://geodesic.mathdoc.fr/item/TMF_2023_216_1_a11/