Geodesic
On the solvability of one class of two-dimensional Urysohn integral equations
Matematičeskie trudy, Tome 20 (2017) no. 2, pp. 193-205

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We study one class of nonlinear Urysohn integral equations in a quadrant of the plane. It is assumed that, for the corresponding two-dimensional Urysohn operator, some Hammerstein operator with power nonlinearity serves as a minorant in the sense of M. A. Krasnosel'ski­ĭ. We prove the existence of a nonnegative (nontrivial) and bounded solution for such equations. 
@article{MT_2017_20_2_a7,
     author = {Kh. A. Khachatryan},
     title = {On the solvability of one class of two-dimensional {Urysohn} integral equations},
     journal = {Matemati\v{c}eskie trudy},
     pages = {193--205},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2017_20_2_a7/}
}
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Kh. A. Khachatryan. On the solvability of one class of two-dimensional Urysohn integral equations. Matematičeskie trudy, Tome 20 (2017) no. 2, pp. 193-205. http://geodesic.mathdoc.fr/item/MT_2017_20_2_a7/