2024 Volume 14 Issue 1
Article Contents
Article navigation > Journal of Applied Analysis & Computation > 2024 > 14(1): 560-578
Next Article Previous Article

Peiguang Wang, Beibei Li, Junyan Bao. AVERAGING METHOD FOR MULTI-POINT BOUNDARY VALUE PROBLEMS OF SET-VALUED FUNCTIONAL DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 560-578. doi: 10.11948/20230309
Citation: Peiguang Wang, Beibei Li, Junyan Bao. AVERAGING METHOD FOR MULTI-POINT BOUNDARY VALUE PROBLEMS OF SET-VALUED FUNCTIONAL DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 560-578. doi: 10.11948/20230309
shu

AVERAGING METHOD FOR MULTI-POINT BOUNDARY VALUE PROBLEMS OF SET-VALUED FUNCTIONAL DIFFERENTIAL EQUATIONS

  • 1.

    School of Mathematics and Information Science, Hebei University, 071002, China

    Abstract

  • In this paper, we present a study of the set-valued functional differential equations, of which the right functions are the product of two terms. First, the global averaging method of the equations is considered. Then, by introducing the concept of semi-deviation metric, we consider the averaging method of the above equations for the case in which the limit of a method of an average does not exist. The proof is based on the analysis of support functions and measurable choice sets.

    MSC: 34B08, 34C29, 34D05
    • FullText(HTML)
  • 加载中
    • References
  • [1] Z. Guo and J. Llibre, Limit cycles of a class of discontinuous piecewise differential systems separated by the curve y = x(n) via averaging theory, International Journal of Bifurcation and Chaos, 2022, 32(12), 2250187. doi: 10.1142/S0218127422501875

    CrossRef Google Scholar

    [2] A. Khastan, R. Rodríguez-López and M. Shahidi, New differentiability concepts for set-valued functions and applications to set differential equations, Information Sciences, 2021, 575(2), 355–378.

    Google Scholar

    [3] V. Kolmanovskii and A. Myshkis, Applied Theory of Functional Differential Equations, Springer Science and Business Media, 2010.

    Google Scholar

    [4] A. Kolpakov, Averaging in a certain ordinary differential equation, Siberian Mathematical Journal, 1983, 24(3), 367–372.

    Google Scholar

    [5] M. Lakrib, T. Kherraz and A. Bourada, Averaging for ordinary differential equations perturbed by a small parameter, Mathematica Bohemica, 2016, 141(2), 143–151. doi: 10.21136/MB.2016.12

    CrossRef Google Scholar

    [6] M. Lakrib and T. Sari, Time averaging for ordinary differential equations and retarded functional differential equations, Electronic Journal of Differential Equations, 2010, 2010(40), 596–606.

    Google Scholar

    [7] V. Lakshmikantham, T. G. Bhaskar and J. V. Devi, Theory of Set Differential Equations in Metric Spaces, Cambridge Scientific Publishers, 2006.

    Google Scholar

    [8] V. Lakshmikantham and R. N. Mohapatra, Theory of Fuzzy Differential Equations and Inclusions, CRC press, 2003.

    Google Scholar

    [9] C. Liu, X. Liu, Z. Yang, et al., New stability results of generalized impulsive functional differential equations, Science China Information Sciences, 2022, 65(14), 1–3.

    Google Scholar

    [10] D. D. Novaes, An averaging result for periodic solutions of caratheodory differential equations, Proceedings of the American Mathematical Society, 2022, 150(7), 2945–2954. doi: 10.1090/proc/15810

    CrossRef Google Scholar

    [11] V. A. Plotnikov and O. D. Kichmarenko, Averaging of controlled equations with hukuhara derivative, Nonlinear Oscillations, 2006, 9(3), 365–374. doi: 10.1007/s11072-006-0050-1

    CrossRef Google Scholar

    [12] V. A. Plotnikov and O. D. Kichmarenko, A note on the averaging method for differential equations with maxima, Iranian Journal of Optimization, 2009, 1(2), 132–140.

    Google Scholar

    [13] V. A. Plotnikov and T. A. Komleva, On the averaging of set differential inclusions in a semilinear metric space when the average of the right-hand side is absent, International Journal of Nonlinear Science, 2011, 11(1), 28–34.

    Google Scholar

    [14] V. A. Plotnikov and P. Rashkov, Averaging in differential equations with hukuhara derivative and delay, Functional Differential Equations, 2001, 8(3–4), 371–381.

    Google Scholar

    [15] V. A. Plotnikov and V. Savchenko, On averaging of differential inclusions in the case where the average of the right-hand side does not exist, Ukrainian Mathematical Journal, 1996, 48(11), 1779–1784. doi: 10.1007/BF02529499

    CrossRef Google Scholar

    [16] V. Popov, Elliptic functional differential equations with degenerations, Lobachevskii Journal of Mathematics, 2020, 41(5), 869–894. doi: 10.1134/S199508022005011X

    CrossRef Google Scholar

    [17] L. E. Rossovskii and A. A. Tovsultanov, Functional-differential equations with dilation and symmetry, Siberian Mathematical Journal, 2022, 63(4), 758–768. doi: 10.1134/S0037446622040164

    CrossRef Google Scholar

    [18] N. Skripnik, Averaging of impulsive differential inclusions with fuzzy right-hand side when the average is absent, Asian-European Journal of Mathematics, 2015, 8(4), 1550086. doi: 10.1142/S1793557115500862

    CrossRef Google Scholar

    [19] N. Skripnik, Three-step averaging scheme for set-valued differential equations with generalized derivative, Journal of Mathematical Sciences, 2019, 236(3), 333–342.

    Google Scholar

    [20] M. Spadini, Periodic perturbations of a class of functional differential equations, Journal of Dynamics and Differential Equations, 2022, 34(1), 535–553.

    Google Scholar

    • Supplements
    • Cited by
Export Citation
PDF
XML

Article Metrics

Article views(1360) PDF downloads(367) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Published by Wilmington Scientific Publisher