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Nonlinear Functional-Differential Equation of Neutral Type with Linear Deviation of the Argument

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We obtain new properties of the solutions of a nonlinear functional-differential equation of neutral type with linear deviation of the argument encountered in quantum mechanics in the investigation of self-similar potentials and coherent states. Namely, we establish the conditions under which the solution of the Cauchy problem is either given on the entire positive semiaxis or exists only on a finite interval and study its asymptotic behavior. In addition, under certain conditions, for a sufficiently smooth solution, we present asymptotic representations of both the solution itself and its derivatives with an accuracy that depends on the smoothness of the solution.

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References

  1. V. P. Spiridonov, “Self-similar potentials in quantum mechanics and coherent states,” Phys. Particles Nuclei, 52, 274–289 (2021).

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivs’ka Str., 3, Kyiv, 01024, Ukraine

    G. P. Pelyukh & D. V. Bel’skii

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  1. G. P. Pelyukh
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  2. D. V. Bel’skii
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Correspondence to D. V. Bel’skii.

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Translated from Neliniini Kolyvannya, Vol. 25, No. 1, pp. 59–71, January–March, 2022.

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Pelyukh, G.P., Bel’skii, D.V. Nonlinear Functional-Differential Equation of Neutral Type with Linear Deviation of the Argument. J Math Sci 274, 60–75 (2023). https://doi.org/10.1007/s10958-023-06571-2

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  • DOI: https://doi.org/10.1007/s10958-023-06571-2

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