IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i10p1768-d427339.html
   My bibliography  Save this article

Existence and Uniqueness of Solutions for the p ( x )-Laplacian Equation with Convection Term

Author

Listed:
  • Bin-Sheng Wang

    (College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China)

  • Gang-Ling Hou

    (College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China)

  • Bin Ge

    (College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China)

Abstract

In this paper, we consider the existence and uniqueness of solutions for a quasilinear elliptic equation with a variable exponent and a reaction term depending on the gradient. Based on the surjectivity result for pseudomonotone operators, we prove the existence of at least one weak solution of such a problem. Furthermore, we obtain the uniqueness of the solution for the above problem under some considerations. Our results generalize and improve the existing results.

Suggested Citation

  • Bin-Sheng Wang & Gang-Ling Hou & Bin Ge, 2020. "Existence and Uniqueness of Solutions for the p ( x )-Laplacian Equation with Convection Term," Mathematics, MDPI, vol. 8(10), pages 1-10, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1768-:d:427339
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/10/1768/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/10/1768/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    2. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    3. Weihong Xie & Haibo Chen, 2018. "Existence and multiplicity of solutions for p(x)‐Laplacian equations in RN," Mathematische Nachrichten, Wiley Blackwell, vol. 291(16), pages 2476-2488, November.
    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. Agnieszka Kurdyś-Kujawska & Agnieszka Sompolska-Rzechuła & Joanna Pawłowska-Tyszko & Michał Soliwoda, 2021. "Crop Insurance, Land Productivity and the Environment: A Way forward to a Better Understanding," Agriculture, MDPI, vol. 11(11), pages 1-17, November.
    2. van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 2005. "Computing Integral Solutions of Complementarity Problems," Discussion Paper 2005-5, Tilburg University, Center for Economic Research.
    3. Wenfeng Chi & Yuanyuan Zhao & Wenhui Kuang & Tao Pan & Tu Ba & Jinshen Zhao & Liang Jin & Sisi Wang, 2021. "Impact of Cropland Evolution on Soil Wind Erosion in Inner Mongolia of China," Land, MDPI, vol. 10(6), pages 1-16, June.
    4. Yulin Zhao, 2012. "Positive Solutions for ( k , n − k ) Conjugate Multipoint Boundary Value Problems in Banach Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-18, August.
    5. Nick Middleton & Utchang Kang, 2017. "Sand and Dust Storms: Impact Mitigation," Sustainability, MDPI, vol. 9(6), pages 1-22, June.
    6. Tarantino, Emanuele & Pavanini, Nicola & Mayordomo, Sergio, 2020. "The Impact of Alternative Forms of Bank Consolidation on Credit Supply and Financial Stability," CEPR Discussion Papers 15069, C.E.P.R. Discussion Papers.
    7. Truong Duong & Nguyen Tan, 2012. "On the existence of solutions to generalized quasi-equilibrium problems," Journal of Global Optimization, Springer, vol. 52(4), pages 711-728, April.
    8. Misbah Haque & Imran Ali, 2016. "Uncertain Environment and Organizational Performance: The Mediating Role of Organizational Innovation," Asian Social Science, Canadian Center of Science and Education, vol. 12(9), pages 124-124, September.
    9. repec:spo:wpmain:info:hdl:2441/2082 is not listed on IDEAS
    10. , & ,, 2015. "Strategy-proofness and efficiency with non-quasi-linear preferences: a characterization of minimum price Walrasian rule," Theoretical Economics, Econometric Society, vol. 10(2), May.
    11. Navid Bayati & Mehdi Savaghebi, 2021. "Protection Systems for DC Shipboard Microgrids," Energies, MDPI, vol. 14(17), pages 1-20, August.
    12. Velloso, Helvia & Vézina, François & Bustillo, Inés, 2006. "The Canadian retirement income system," Documentos de Proyectos 3682, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    13. Jesus M. Carro & Alejandra Traferri, 2014. "State Dependence And Heterogeneity In Health Using A Bias‐Corrected Fixed‐Effects Estimator," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(2), pages 181-207, March.
    14. Nobuyoshi Yamori & Ayami Kobayashi, 2007. "Wealth Effect Of Public Fund Injections To Ailing Banks: Do Deferred Tax Assets And Auditing Firms Matter?," The Japanese Economic Review, Japanese Economic Association, vol. 58(4), pages 466-483, December.
    15. Ngai Fen Cheung & Anshi Pan, 2012. "Childbirth experience of migrants in China: A systematic review," Nursing & Health Sciences, John Wiley & Sons, vol. 14(3), pages 362-371, September.
    16. Vladimir Krivtsov & Brian J. D’Arcy & Alejandro Escribano Sevilla & Scott Arthur & Chris Semple, 2021. "Mitigating Polluted Runoff from Industrial Estates by SUDS Retrofits: Case Studies of Problems and Solutions Co-Designed with a Participatory Approach," Sustainability, MDPI, vol. 13(22), pages 1-24, November.
    17. Operations Evaluation Department, 2005. "Capacity Building in Africa : An OED Evaluation of World Bank Support," World Bank Publications - Books, The World Bank Group, number 7468.
    18. Jean-Pierre Allegret & Alain Sand-Zantman, 2008. "Monetary Integration Issues in Latin America: A Multivariate Assessment," Panoeconomicus, Savez ekonomista Vojvodine, Novi Sad, Serbia, vol. 55(3), pages 279-308, September.
    19. M. Balaj & L. J. Lin, 2013. "Existence Criteria for the Solutions of Two Types of Variational Relation Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 232-246, February.
    20. Werner, Katharina & Graf Lambsdorff, Johann, 2016. "Emotional numbing and lessons learned after a violent conflict - Experimental evidence from Ambon, Indonesia," Passauer Diskussionspapiere, Volkswirtschaftliche Reihe V-74-16, University of Passau, Faculty of Business and Economics.
    21. Wong, Patricia J.Y., 2015. "Eigenvalues of a general class of boundary value problem with derivative-dependent nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 908-930.

    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:gam:jmathe:v:8:y:2020:i:10:p:1768-:d:427339. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.