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2019 Fixed point results in set $P_{h,e}$ with applications to fractional differential equations
Lingling Zhang, Hui Wang, Xiaoqiang Wang
Topol. Methods Nonlinear Anal. 54(2A): 537-566 (2019). DOI: 10.12775/TMNA.2019.052

Abstract

In this paper, without assuming operators to be continuous or compact, by employing monotone iterative technique on ordered Banach space, we at first establish new fixed point theorems for some kinds of nonlinear mixed monotone operators in set $P_{h,e}$. Then, we study a new form of fractional two point boundary value problem depending on a certain constant and give the existence and uniqueness of solutions. We also show that the unique solution exists in set $P_{h,e}$ or $P_{h}$ and can be uniformly approximated by constructing two iterative sequences for any initial values. At the end, a concrete example is given to illustrate our abstract results. The conclusions of this article enrich the fixed point theorems and provide new methods to deal with nonlinear differential equations.

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Lingling Zhang. Hui Wang. Xiaoqiang Wang. "Fixed point results in set $P_{h,e}$ with applications to fractional differential equations." Topol. Methods Nonlinear Anal. 54 (2A) 537 - 566, 2019. https://doi.org/10.12775/TMNA.2019.052

Information

Published: 2019
First available in Project Euclid: 7 October 2019

zbMATH: 07198796
MathSciNet: MR4061309
Digital Object Identifier: 10.12775/TMNA.2019.052

Rights: Copyright © 2019 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.54 • No. 2A • 2019
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