IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v110y2018icp209-215.html
   My bibliography  Save this article

Monotone iterative method for the periodic boundary value problems of impulsive evolution equations in Banach spaces

Author

Listed:
  • Li, Baolin
  • Gou, Haide

Abstract

We use a monotone iterative method in the presence of lower and upper solutions to discuss the existence and uniqueness of mild solutions for the boundary value problem of impulsive evolution equation in an ordered Banach space Eu′(t)+Au(t)=f(t,u(t),Fu(t),Gu(t)),t∈J,t≠tk,Δu|t=tk=Ik(u(tk)),k=1,2,⋯,m,u(0)=u(ω),where A: D(A) ⊂ E → E is a closed linear operator and −A generates a C0-semigroup T(t)(t ≥ 0) in E. Under wide monotonicity conditions and the non-compactness measure condition of the nonlinearity f, we obtain the existence of extremal mild solutions and a unique mild solution between lower and upper solutions requiring only that −A generate a C0-semigroup.

Suggested Citation

  • Li, Baolin & Gou, Haide, 2018. "Monotone iterative method for the periodic boundary value problems of impulsive evolution equations in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 209-215.
    • Handle: RePEc:eee:chsofr:v:110:y:2018:i:c:p:209-215
    DOI: 10.1016/j.chaos.2018.03.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077918301231
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2018.03.027?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. World Bank, 2002. "Costa Rica : Social Spending and the Poor, Volume 1. Summary of Issues and Recommendations with Executive Summary," World Bank Publications - Reports 15330, The World Bank Group.
    2. Hernández-Hernández, M.E. & Kolokoltsov, V.N. & Toniazzi, L., 2017. "Generalised fractional evolution equations of Caputo type," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 184-196.
    3. Simon Levin & Anastasios Xepapadeas, 2021. "On the Coevolution of Economic and Ecological Systems," Annual Review of Resource Economics, Annual Reviews, vol. 13(1), pages 355-377, October.
    4. Hoang Ngoc Tuan, 2015. "Boundedness of a Type of Iterative Sequences in Two-Dimensional Quadratic Programming," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 234-245, January.
    5. Wang, Daojuan & Hain, Daniel S. & Larimo, Jorma & Dao, Li T., 2020. "Cultural differences and synergy realization in cross-border acquisitions," International Business Review, Elsevier, vol. 29(3).
    6. Zhou, H. & Uhlaner, L.M., 2009. "Knowledge Management in the SME and its Relationship to Strategy, Family Orientation and Organization Learning," ERIM Report Series Research in Management ERS-2009-026-ORG, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    7. Turpie, J.K. & Marais, C. & Blignaut, J.N., 2008. "The working for water programme: Evolution of a payments for ecosystem services mechanism that addresses both poverty and ecosystem service delivery in South Africa," Ecological Economics, Elsevier, vol. 65(4), pages 788-798, May.
    8. Koichi Hamada & Asahi Noguchi, 2005. "The Role of Preconceived Ideas in Macroeconomic Policy: Japan's Experiences in the Two Deflationary Periods," Working Papers 908, Economic Growth Center, Yale University.
    9. Jingyi Xue, 2018. "Fair division with uncertain needs," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(1), pages 105-136, June.
    10. Dipak R. Pant, 2013. "Managing the global waste in the 21st century: As an anthropologist views it," LIUC Papers in Economics 263, Cattaneo University (LIUC).
    11. van der Laan, Gerard & Talman, Dolf & Yang, Zaifu, 2011. "Solving discrete systems of nonlinear equations," European Journal of Operational Research, Elsevier, vol. 214(3), pages 493-500, November.
    12. Richard ANKER, 2006. "Poverty lines around the world: A new methodology and internationally comparable estimates," International Labour Review, International Labour Organization, vol. 145(4), pages 279-307, December.
    13. X. F. Li & J. Z. Zhang, 2006. "Necessary Optimality Conditions in Terms of Convexificators in Lipschitz Optimization," Journal of Optimization Theory and Applications, Springer, vol. 131(3), pages 429-452, December.
    14. Popli, Manish & Akbar, Mohammad & Kumar, Vikas & Gaur, Ajai, 2016. "Reconceptualizing cultural distance: The role of cultural experience reserve in cross-border acquisitions," Journal of World Business, Elsevier, vol. 51(3), pages 404-412.
    15. Quah Chee-Heong, 2019. "China’s Dollar-linked Hong Kong during the Global Crisis," Apuntes del Cenes, Universidad Pedagógica y Tecnológica de Colombia, vol. 38(67), pages 95-121, February.
    16. Lan, Heng-you, 2021. "Approximation-solvability of population biology systems based on p-Laplacian elliptic inequalities with demicontinuous strongly pseudo-contractive operators," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    17. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2020. "On the difficulty of budget allocation in claims problems with indivisible items of different prices," ThE Papers 20/09, Department of Economic Theory and Economic History of the University of Granada..
    18. Slotnick, Susan A., 2011. "Order acceptance and scheduling: A taxonomy and review," European Journal of Operational Research, Elsevier, vol. 212(1), pages 1-11, July.
    19. Winfried Osthorst, 2020. "Tensions in Urban Transitions. Conceptualizing Conflicts in Local Climate Policy Arrangements," Sustainability, MDPI, vol. 13(1), pages 1-17, December.
    20. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2021. "On the Difficulty of Budget Allocation in Claims Problems with Indivisible Items and Prices," Group Decision and Negotiation, Springer, vol. 30(5), pages 1133-1159, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:110:y:2018:i:c:p:209-215. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.