Geodesic
Questions of the existence and uniqueness of the solution of one class of nonlinear integral equations on the whole line
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 26 (2022) no. 3, pp. 446-479

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We consider a class of nonlinear integral equations with a stochastic and symmetric kernel on the whole line. With certain particular representations of the kernel and nonlinearity, equations of the mentioned type arise in many branches of mathematical natural science. In particular, such equations occur in the theory $p$-adic strings, in the kinetic theory of gases, in mathematical biology and in the theory of radiative transfer. Constructive existence theorems are proved for non-negative non-trivial and bounded solutions under various restrictions on the function describing the nonlinearity in the equation. Under additional restrictions on the kernel and on the nonlinearity, a uniqueness theorem is also proved in a certain class of bounded and non-negative functions that have a finite limit in $\pm\infty.$ At the end, specific applied examples of the kernel and non-linearity are given that satisfy to all restrictions of the proven statements.
Keywords: monotonicity, successive approximations, bounded solution, Caratheodory condition.
Mots-clés : convergence, solution limit 
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     author = {Kh. A. Khachatryan and H. S. Petrosyan},
     title = {Questions of the existence and uniqueness of the solution of one class of nonlinear integral equations on the whole line},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {446--479},
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Kh. A. Khachatryan; H. S. Petrosyan. Questions of the existence and uniqueness of the solution of one class of nonlinear integral equations on the whole line. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 26 (2022) no. 3, pp. 446-479. http://geodesic.mathdoc.fr/item/VSGTU_2022_26_3_a2/