Singularly perturbed integro-differential equations with degenerate Hammersteins kernel
Bobodzhanova M.A. Kalimbetov B.T. Safonov V.F.
2024E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2024#116Issue 457 - 68 pp.
Singularly perturbed integro-differential equations with degenerate kernels are considered. It is shown that in the linear case these problems are always uniquely solvable with continuous coefficients, while nonlinear problems either have no real solutions at all or have several of them. For linear problems, the results of Bobojanova are refined; in particular, necessary and sufficient conditions are given for the existence of a finite limit of their solutions as the small parameter tends to zero and sufficient conditions under which the passage to the limit to the solution of the degenerate equation is possible.
analytic function , degenerate kernel , Fredholms equations , Hammersteins equation , Laurents series , passage to the limit , singularly perturbed , the Maple program
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