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- Title
The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems.
- Authors
Lishan Liu; Xinqiu Zhang; Juan Jiang; Yonghong Wu
- 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) = x 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.
- Subjects
NUMERICAL solutions to operator equations; BANACH spaces
- Publication
Journal of Nonlinear Sciences & Applications (JNSA), 2016, Vol 9, Issue 5, p2943
- ISSN
2008-1898
- Publication type
Article
- DOI
10.22436/jnsa.009.05.87