Geodesic
The Cauchy problem with a parameter perturbed by a linear functional
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV", Voronezh, April 26-30, 2024, Part 3, Tome 237 (2024), pp. 10-17

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In this paper, we consider a Cauchy problem with a parameter perturbed by a linear functional. For any value of the parameter, the problem has a trivial solution. We obtain necessary and sufficient conditions for values of the parameter such that in their neighborhoods nontrivial solutions in the class of real continuous functions exist. A method of constructing such solutions is proposed.
Keywords: linear functional, Cauchy problem, Newton diagram, Stieltjes integral
Mots-clés : bifurcation point 
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     author = {L. D. Dreglea Sidorov and N. A. Sidorov},
     title = {The {Cauchy} problem with a parameter perturbed by a linear functional},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {10--17},
     publisher = {mathdoc},
     volume = {237},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2024_237_a1/}
}
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L. D. Dreglea Sidorov; N. A. Sidorov. The Cauchy problem with a parameter perturbed by a linear functional. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV", Voronezh, April 26-30, 2024, Part 3, Tome 237 (2024), pp. 10-17. http://geodesic.mathdoc.fr/item/INTO_2024_237_a1/