Research article

Reversed S -shaped connected component for second-order periodic boundary value problem with sign-changing weight

  • Received: 25 April 2020 Accepted: 06 July 2020 Published: 15 July 2020
  • MSC : 34B10, 34B18

  • In this paper, we consider the existence of an reversed S -shaped connected component in the set of positive solutions for second order periodic boundary value problem with a sign-changing weight function. By bifurcation technique, we identify the interval of bifurcation parameter in which the periodic boundary value problem has one or two or three positive solutions according to the asymptotic behavior of f at 0 and ∞.

    Citation: Liangying Miao, Zhiqian He. Reversed S -shaped connected component for second-order periodic boundary value problem with sign-changing weight[J]. AIMS Mathematics, 2020, 5(6): 5884-5892. doi: 10.3934/math.2020376

    Related Papers:

  • In this paper, we consider the existence of an reversed S -shaped connected component in the set of positive solutions for second order periodic boundary value problem with a sign-changing weight function. By bifurcation technique, we identify the interval of bifurcation parameter in which the periodic boundary value problem has one or two or three positive solutions according to the asymptotic behavior of f at 0 and ∞.


    加载中


    [1] F. M. Atici, G. S. Guseinov, On the existence of positive solutions for nonlinear differential equations with periodic boundary conditions, J. Comput. Appl. Math., 132 (2001), 341-356. doi: 10.1016/S0377-0427(00)00438-6
    [2] A. Boscaggin, F. Zanolin, Pairs of positive periodic solutions of second order nonlinear equations with indefinite weight, J. Differ. Equations, 252 (2012), 2900-2921. doi: 10.1016/j.jde.2011.09.011
    [3] A. Constantin, A general-weighted Sturm-Liouville problem, Ann. Sci. Ec. Norm. Super., 24 (1997), 767-782.
    [4] G. Dai, R. Ma, H. Wang, Eigenvalues, bifurcation and one-sign solutions for the periodic p-Laplacian, Commun. Pure Appl. Anal., 12 (2013), 2839-2872. doi: 10.3934/cpaa.2013.12.2839
    [5] J. R. Graef, L. Kong, H. Wang, Existence, multiplicity, and dependence on a parameter for a periodic boundary value problem, J. Differ. Equations, 245 (2008), 1185-1197.
    [6] R. Hakl, M. Zamora, Periodic solutions to second-order indefinite singular equations, J. Differ. Equations, 263 (2017), 451-469. doi: 10.1016/j.jde.2017.02.044
    [7] X. Hao, L. Liu,Y. Wu, Existence and multiplicity results for nonlinear periodic boundary value problems, Nonlinear Anal., 72 (2010), 3635-3642. doi: 10.1016/j.na.2009.12.044
    [8] Z. He, R. Ma, M. Xu, Positive solutions for a class of semipositone periodic boundary value problems via bifurcation theory, Electron. J. Qual. Theory Differ. Equ., 29 (2019), 1-15.
    [9] Z. He, R. Ma, M. Xu, Three positive solutions for second-order periodic boundary value problems with sign-changing weight, Bound. Value Probl., 93 (2018), 1-17.
    [10] A. Lomtatidze, J. Šremr, On periodic solutions to second-order Duffing type equations, Nonlinear Anal. Real, 40 (2018), 215-242. doi: 10.1016/j.nonrwa.2017.09.001
    [11] R. Ma, Y. An, Global structure of positive solutions for nonlocal boundary value problems involving integral conditions, Nonlinear Anal., 71 (2009), 4364-4376. doi: 10.1016/j.na.2009.02.113
    [12] R. Ma, J. Xu, X. Han, Global bifurcation of positive solutions of a second-order periodic boundary value problem with indefinite weight, Nonlinear Anal., 74 (2011), 3379-3385. doi: 10.1016/j.na.2011.02.013
    [13] R. Ma, C. Gao, R. Chen, Existence of positive solutions of nonlinear second-order periodic boundary value problems, Bound. Value Probl., 2010 (2010), 1-18. doi: 10.1155/2010/728101
    [14] R. Ma, J. Xu, X. Han, Global structure of positive solutions for superlinear second-order periodic boundary value problems, Appl. Math. Comput., 218 (2012), 5982-5988.
    [15] N. S. Papageorgiou, C. Vetro, F. Vetro, Solutions for parametric double phase Robin problems, Asymptotic Anal., 1 (2020), 1-12.
    [16] N. S. Papageorgiou, C. Vetro, F. Vetro, Parameter dependence for the positive solutions of nonlinear, nonhomogeneous Robin problems, RACSAM, 114 (2020), 1-29. doi: 10.1007/s13398-019-00732-2
    [17] I. Sim, S. Tanaka, Three positive solutions for one-dimensional p-Laplacian problem with signchanging weight, Appl. Math. Lett., 49 (2015), 42-50. doi: 10.1016/j.aml.2015.04.007
    [18] J. Xu, R. Ma, Bifurcation from interval and positive solutions for second order periodic boundary value problems, Appl. Math. Comput., 216 (2010), 2463-2471.
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(2656) PDF downloads(194) Cited by(1)

Article outline

Figures and Tables

Figures(2)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog