IJAM: Volume 38, No. 4 (2025)

DOI: 10.12732/ijam.v38i4.3

NONLINEAR SINGULARLY PERTURBED
INTEGRO-DIFFERENTIAL EQUATIONS WITH
A ZERO OPERATOR OF THE DIFFERENTIAL
PART AND EXPONENTIALLY OSCILLATING
INHOMOGENEITY

Abdukhafiz Bobodzhanov¹, Burkhan Kalimbetov^2,*, Valeriy Safonov¹, Dinmukhambet Sapakov²

¹National Research University, MPEI
Krasnokazarmennaya 14, Moscow, 111250, RUSSIA
²Kuatbekov People's Friendship University
Tole bi 32b, Shymkent, 160011, KAZAKHSTAN

Abstract. 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

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How to cite this paper?
DOI: 10.12732/ijam.v38i4.3
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2025
Volume: 38
Issue: 4

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