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A Bifurcation of Solutions of Nonlinear Fredholm Inclusions Involving CJ-Multimaps with Applications to Feedback Control Systems

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Abstract

In this paper, by applying the oriented coincidence index for a pair consisting of a nonlinear Fredholm operator and a CJ-multimap, we prove a global bifurcation theorem for solutions of families of inclusions with such maps. The method of guiding functions is used to calculate the oriented coincidence index for a class of feedback control systems. This characteristic allows to obtain the existence result for periodic trajectories of such systems. From the other side, it opens the possibility to apply the abstract bifurcation result to the study of qualitative behavior of branches of periodic trajectories.

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Authors and Affiliations

  1. PetroVietNam University, Ba Ria - Vung Tau, Vietnam

    Nguyen Van Loi

  2. Faculty of Physics and Mathematics, Voronezh State Pedagogical University, 394043, Voronezh, Russia

    Valeri Obukhovskii

  3. Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung, 807, Taiwan

    Jen-Chih Yao

  4. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 804, Taiwan

    Jen-Chih Yao

Authors
  1. Nguyen Van Loi
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  2. Valeri Obukhovskii
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  3. Jen-Chih Yao
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Correspondence to Jen-Chih Yao.

Additional information

This research was partially supported by the grant NSC 98-2923-E-110-003-MY3 and the Taiwan NSC–Russian FBR Grant 09-01-92003. The work of V. Obukhovskii is partially supported by the Russian FBR Grants 11-01-00328 and 12-01-00392. The work of J. C. Yao was partially supported by the Grant NSC 99-2221-E-037-007-MY3.

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Loi, N.V., Obukhovskii, V. & Yao, JC. A Bifurcation of Solutions of Nonlinear Fredholm Inclusions Involving CJ-Multimaps with Applications to Feedback Control Systems. Set-Valued Var. Anal 21, 247–269 (2013). https://doi.org/10.1007/s11228-012-0226-z

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