Existence and uniqueness of fixed points for mixed monotone operators with applications

2006 ◽  
Vol 65 (10) ◽  
pp. 1913-1924 ◽  
Author(s):  
Yuexiang Wu ◽  
Zhandong Liang
Keyword(s):  
Fixed Points ◽  
Existence And Uniqueness ◽  
Monotone Operators ◽  
Mixed Monotone Operators

scholarly journals Positive Solutions of a Nonlinear Parabolic Partial Differential Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Chengbo Zhai ◽  
Shunyong Li
Keyword(s):  
Differential Equation ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Monotone Operators ◽  
Parabolic Partial Differential Equation ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Nonlinear Parabolic ◽  
Mixed Monotone Operators

We deal with the existence and uniqueness of positive solutions to a class of nonlinear parabolic partial differential equations, by using some fixed point theorems for mixed monotone operators with perturbation.

Existence and uniqueness of positive solutions for boundary value problems of fractional differential equations

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2675-2682 ◽  
Author(s):  
Hojjat Afshari ◽  
Hamidreza Marasi ◽  
Hassen Aydi
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Monotone Operators ◽  
Fractional Differential ◽  
Mixed Monotone Operators

By using fixed point results of mixed monotone operators on cones and the concept of ?-concavity, we study the existence and uniqueness of positive solutions for some nonlinear fractional differential equations via given boundary value problems. Some concrete examples are also provided illustrating the obtained results.

scholarly journals Existence and Uniqueness of Positive Solutions for a Class of Nonlinear Fractional Differential Equations with Singular Boundary Value Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yan Debao
Keyword(s):  
Fixed Point ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Nonlinear Function ◽  
Monotone Operators ◽  
Singular Boundary ◽  
Temporal Variables ◽  
Fractional Differential ◽  
Mixed Monotone Operators

This paper focuses on a singular boundary value (SBV) problem of nonlinear fractional differential (NFD) equation defined as follows: D 0 + β υ τ + f τ , υ τ = 0 , τ ∈ 0,1 , υ 0 = υ ′ 0 = υ ″ 0 = υ ″ 1 = 0 , where 3 < β ≤ 4 , D 0 + β is the standard Riemann–Liouville fractional (RLF) derivative. The nonlinear function f τ , υ τ might be singular on the spatial and temporal variables. This paper proves that a positive solution to the SBV problem exists and is unique, taking advantage of Green’s function through a fixed-point (FP) theory on cones and mixed monotone operators.

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