Existence and Uniqueness of Positive Solutions for a Class of Second-Order Nonlinear Differential Systems

2021 ◽  
Vol 11 (06) ◽  
pp. 1211-1220
Author(s):  
阳 杨
Keyword(s):  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Second Order ◽  
Differential Systems ◽  
Nonlinear Differential Systems

scholarly journals Nonlinear Sum Operator Equations with a Parameter and Application to Second-Order Three-Point BVPs

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Wen-Xia Wang ◽  
Xi-Lan Liu ◽  
Piao-Piao Shi
Keyword(s):  
Nonlinear Analysis ◽  
Boundary Value Problems ◽  
Banach Spaces ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Critical Value ◽  
Second Order ◽  
Point Boundary ◽  
Operator Equations

A class of nonlinear sum operator equations with a parameter on order Banach spaces were considered. The existence and uniqueness of positive solutions for this kind of operator equations and the dependence of solutions on the parameter have been obtained by using the properties of cone and nonlinear analysis methods. The critical value of the parameter was estimated. Further, the application to some nonlinear three-point boundary value problems was given to show the significance of the discussion.

scholarly journals Existence-uniqueness of positive solutions to nonlinear impulsive fractional differential systems and optimal control

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shu Song ◽  
Lingling Zhang ◽  
Bibo Zhou ◽  
Nan Zhang
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Mixed Monotone Operator ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential

Abstract In this thesis, we investigate a kind of impulsive fractional order differential systems involving control terms. By using a class of φ-concave-convex mixed monotone operator fixed point theorem, we obtain a theorem on the existence and uniqueness of positive solutions for the impulsive fractional differential equation, and the optimal control problem of positive solutions is also studied. As applications, an example is offered to illustrate our main results.

scholarly journals Positive Solutions for Second-Order Nonlinear Ordinary Differential Systems with Two Parameters

2011 ◽  
Vol 2011 ◽  
pp. 1-13
Author(s):  
Lan Sun ◽  
Yukun An ◽  
Min Jiang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Point Theorem ◽  
Second Order ◽  
Differential Systems ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions ◽  
Two Parameters

By using fixed-point theorem and under suitable conditions, we investigate the existence and multiplicity positive solutions to the following systems: , where are four positive constants and , , and . We derive two explicit intervals of and , such that the existence and multiplicity of positive solutions for the systems is guaranteed.

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