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Branching of solutions of the problem of synthesis of a linear antenna with given directional amplitude diagram in a Hölder space

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Abstract

We investigate the branching of solutions of a nonlinear integral equation of the Hammerstein type which arises in the problem of synthesis of a linear antenna with given directional amplitude diagram. Systems of transcendental equations for determination of branching points of various types are deduced, and the number of branched solutions and their qualitative characteristics are analyzed.

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References

  1. M. I. Andriichuk, N. N. Voitovich, P. A. Savenko, and V. P. Tkachuk,Synthesis of Antennas by the Directional Amplitude Diagram: Numerical Methods and Algorithms [in Russian], Naukova Dumka, Kiev (1993).

    Google Scholar 

  2. Kh. G. Bzhikhatlov, “Boudary-value problem for a degenerating hyperbolic equation and singular integral equations of the third kind,”Differents. Uravn.,7, No. 1, 3–14 (1971).

    MATH  Google Scholar 

  3. M. M. Vainberg and V. A. Trenogin,Theory of Branching of Solutions of Nonlinear Equations [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  4. N. N. Voitovich and P. A. Savenko, “Branching of solutions of the problem of synthesis of antennas by a given directional amplitude diagram,”Radiotekh. Élektron.,21, No. 4, 723–729 (1976).

    Google Scholar 

  5. P. P. Zabreiko, A. I. Koshelev, M. A. Krasnosel'skii, et al.,Integral Equations [in Russian], Nauka, Moscow (1968).

    Google Scholar 

  6. P. A. Savenko, “On branching of solutions, of problems of synthesis of radiating systems with flat aperture by a given directional amplitude diagram,”Izv. Vyssh. Uchebn. Zaved., Radiofiz.,29, No. 3, 339–345 (1986).

    Google Scholar 

  7. P. A. Savenko, “Synthesis of antennas by a given directional amplitude diagram with the use of functionals of the Tikhonov type,”Izv. Vyssh. Uchebn. Zaved., Radioélektron.,39, No. 2, 35–50 (1996).

    Google Scholar 

  8. P. A. Savenko, “Synthesis of linear antenna arrays by a given directional amplitude diagram,”Izv. Vyssh. Uchebn. Zaved., Radiofiz.,22, No. 12, 1498–1504 (1979).

    Google Scholar 

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Authors
  1. P. O. Savenko
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Additional information

Pidtryhach Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences, L'viv. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 2, pp. 35–44, April–June, 1998.

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Savenko, P.O. Branching of solutions of the problem of synthesis of a linear antenna with given directional amplitude diagram in a Hölder space. J Math Sci 99, 1557–1568 (2000). https://doi.org/10.1007/BF02674179

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  • DOI: https://doi.org/10.1007/BF02674179

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