NONLINEAR SINGULARLY PERTURBED INTEGRO-DIFFERENTIAL EQUATIONS WITH A ZERO OPERATOR OF THE DIFFERENTIAL PART AND EXPONENTIALLY OSCILLATING INHOMOGENEITY
Bobodzhanov A. Kalimbetov B. Safonov V. Sapakov D.
2025Diogenes Co. Ltd.
International Journal of Applied Mathematics
2025#38Issue 4475 - 495 pp.
In this paper, we consider a nonlinear integro-differential problem with a zero operator of the differential part, the integral operator of which contains a rapidly changing kernel, and the right-hand side depends on a rapidly oscillating exponent. This work is a continuation of the research carried out earlier for a similar linear system with a rapidly changing kernel. In the nonlinear case, the conditions for the solvability of the corresponding iterative problems, as in the linear case, will have the form not of differential (as was the case in problems with a nonzero operator of the differential part), but of integro-differential equations, and the formation of these equations is played by nonlinearity and rapidly oscillating inhomogeneity.
integral regularization , integro-differential equation , regularization problems , singular perturbation , solvability of iterative problems
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National Research University, MPEI Krasnokazarmennaya 14, Moscow, 111250, Russian Federation
Kuatbekov Peoples’ Friendship University Tole bi 32b, Shymkent, 160011, Kazakhstan
National Research University
Kuatbekov Peoples’ Friendship University Tole bi 32b
10 лет помогаем публиковать статьи Международный издатель
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