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    The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems

    Access Status
    Fulltext not available
    Authors
    Liu, Lishan
    Zhang, X.
    Jiang, J.
    Wu, Yong Hong
    Date
    2016
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Liu, L. and Zhang, X. and Jiang, J. and Wu, Y.H. 2016. The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems. Journal of Nonlinear Science and Applications. 9 (5): pp. 2943-2958.
    Source Title
    Journal of Nonlinear Science and Applications
    Additional URLs
    http://www.tjnsa.com/includes/files/articles/Vol9_Iss5_2943--2958_The_unique_solution_of_a_class_of.pdf
    ISSN
    2008-1898
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/39057
    Collection
    • Curtin Research Publications
    Abstract

    In this paper we study a class of operator equations A(x, x) + B(x, x) = x in ordered Banach spaces, where A, B are two mixed monotone operators. Various theorems are established to guarantee the existence of a unique solution to the problem. In addition, associated iterative schemes have been established for finding the approximate solution converging to the fixed point of the problem. We also study the solution of the nonlinear eigenvalue equation A(x, x) + B(x, x) = λx and discuss its dependency to the parameter. Our results extend and improve many known results in this field of study. We have also successfully demonstrated the application of our results to the study of nonlinear fractional differential equations with two-point boundary conditions.

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