scholarly journals New Fixed Point Theorems of Mixed Monotone Operators and Applications to Singular Boundary Value Problems on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-14
Author(s):  
Huiye Xu
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Time Scales ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Monotone Operators ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Mixed Monotone Operators

Singular boundary value problems for P-Laplacian-like equations

1997 ◽  
Vol 127 (5) ◽  
pp. 975-981 ◽  
Author(s):  
D. D. Hai ◽  
Seth F. Oppenheimer
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Nonlinear Boundary Value Problems ◽  
Existence Of Positive Solutions

SynopsisWe consider the existence of positive solutions to a class of singular nonlinear boundary value problems for P-Laplacian-like equations. Our approach is based on the Schauder Fixed-Point Theorem.

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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