The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems
By Lishan Liu, Xinqiu Zhang, Juan Jiang, Yonghong Wu. 2016
55 citations recorded by the source corpus.
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. c ©2016 All rights reserved.
Subfields: Applied Mathematics, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/1150236fa234b133ad903893bbf7129970275bb1
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In Applied Mathematics
In Modeling and Simulation
Citations in the corpus
- New uniqueness results for boundary value problem of fractional differential equation (2018, background): “However, there are few works on the uniqueness for boundary value problems of fractional differential equations [2, 4, 10, 13, 14].”