Geodesic
On the Solvability of a Class of Nonlinear Hammerstein--Stieltjes Integral Equations on the Whole Line
Informatics and Automation, Differential equations and dynamical systems, Tome 308 (2020), pp. 253-264

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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{TRSPY_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 = {Informatics and Automation},
     pages = {253--264},
     publisher = {mathdoc},
     volume = {308},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2020_308_a18/}
}
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Kh. A. Khachatryan; H. S. Petrosyan. On the Solvability of a Class of Nonlinear Hammerstein--Stieltjes Integral Equations on the Whole Line. Informatics and Automation, Differential equations and dynamical systems, Tome 308 (2020), pp. 253-264. http://geodesic.mathdoc.fr/item/TRSPY_2020_308_a18/