scholarly journals Positive solutions of an initial value problem of a delay-self-reference nonlinear differential equation

2020 ◽  
Vol 8 (3) ◽  
pp. 1001-1006
Author(s):  
EL-Sayed A.M.A ◽  
Eman Hamdallah ◽  
Ebead H.R
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Positive Solutions ◽  
Initial Value Problem ◽  
Initial Value ◽  
Self Reference

An iteration method for a nonlinear differential equation describing the convergence to equilibrium in a system of reacting polymers

1981 ◽  
Vol 375 (1763) ◽  
pp. 529-542
Keyword(s):  
Differential Equation ◽  
Initial Data ◽  
Global Solution ◽  
Nonlinear Differential Equation ◽  
Initial Value Problem ◽  
Iteration Method ◽  
Constructive Method ◽  
Convergence To Equilibrium ◽  
Initial Value

A constructive method is presented to give the global solution to a nonlinear initial value problem describing the convergence to equilibrium in a system of reacting polymers. The solution is proved to be unique and continuous with respect to small variations in the initial data.

scholarly journals Positive Solutions of an Initial Value Problem for Nonlinear Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
D. Baleanu ◽  
H. Mohammadi ◽  
Sh. Rezapour
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Positive Solutions ◽  
Initial Value Problem ◽  
Initial Value ◽  
Nonlinear Fractional Differential Equation ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions

We investigate the existence and multiplicity of positive solutions for the nonlinear fractional differential equation initial value problemD0+αu(t)+D0+βu(t)=f(t,u(t)), u(0)=0, 0<t<1, where0<β<α<1, D0+αis the standard Riemann-Liouville differentiation andf:[0,1]×[0,∞)→[0,∞)is continuous. By using some fixed-point results on cones, some existence and multiplicity results of positive solutions are obtained.

scholarly journals Multiplicity Result of Positive Solutions for Nonlinear Differential Equation of Fractional Order

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Yang Liu ◽  
Zhang Weiguo
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Nonlinear Differential Equation ◽  
Positive Solutions ◽  
Fractional Order ◽  
Point Theorem ◽  
Boundary Value ◽  
Order Derivative ◽  
Fractional Order Derivative

We investigate the existence of multiple positive solutions for a class of boundary value problems of nonlinear differential equation with Caputo’s fractional order derivative. The existence results are obtained by means of the Avery-Peterson fixed point theorem. It should be point out that this is the first time that this fixed point theorem is used to deal with the boundary value problem of differential equations with fractional order derivative.

scholarly journals On the existence of positive solutions of a state-dependent neutral functional differential equation with two state-delay functions

2020 ◽  
Vol 4 (2) ◽  
pp. 132-141
Author(s):  
El-Sayed, A. M. A ◽  
◽  
Hamdallah, E. M. A ◽  
Ebead, H. R ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Positive Solutions ◽  
Functional Differential Equation ◽  
Continuous Dependence ◽  
Neutral Functional Differential Equation ◽  
Initial Value ◽  
State Delay ◽  
State Dependent ◽  
Existence Of Positive Solutions ◽  
Functional Differential

In this paper, we study the existence of positive solutions for an initial value problem of a state-dependent neutral functional differential equation with two state-delay functions. The continuous dependence of the unique solution will be proved. Some especial cases and examples will be given.

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