scholarly journals Triple positive solutions for semipositone fractional differential equations m-point boundary value problems with singularities and p–q-order derivatives

2018 ◽  
Vol 23 (6) ◽  
pp. 889-903 ◽  
Author(s):  
Xingqiu Zhang ◽  
Zhuyan Shao ◽  
Qiuyan Zhong ◽  
Zengqin Zhao
Keyword(s):  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Point Boundary ◽  
Height Functions ◽  
Triple Positive Solutions ◽  
Fractional Differential ◽  
Bounded Sets

In this paper, by means of Leggett–Williams and Guo–Krasnosel'skii fixed point theorems, together with height functions of the nonlinearity on different bounded sets, triple positive solutions are obtained for some fractional differential equations with p–q-order derivatives involved in multi-point boundary value conditions. The nonlinearity may not only take negative infinity but also may permit singularities on both the time and the space variables.

scholarly journals Multiple positive solutions for singular higher-order semipositone fractional differential equations with p-Laplacian

2020 ◽  
Vol 25 (5) ◽  
Author(s):  
Qiuyan Zhong ◽  
Xingqiu Zhang ◽  
Lufeng Gu ◽  
Lei Lei ◽  
Zengqin Zhao
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Higher Order ◽  
Multiple Positive Solutions ◽  
Height Functions ◽  
Fractional Differential ◽  
Bounded Sets

In this article, together with Leggett–Williams and Guo–Krasnosel’skii fixed point theorems, height functions on special bounded sets are constructed to obtain the existence of at least three positive solutions for some higher-order fractional differential equations with p-Laplacian. The nonlinearity permits singularities both on the time and the space variables, and it also may change its sign.

scholarly journals Monotone and Concave Positive Solutions to Three-Point Boundary Value Problems of Higher-Order Fractional Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Wenyong Zhong ◽  
Lanfang Wang
Keyword(s):  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Higher Order ◽  
Point Boundary ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Fractional Differential

We study the three-point boundary value problem of higher-order fractional differential equations of the formDc0+ρut+ft, ut=0,0<t<1,2⩽n-1<ρ<n,u′(0)=u′′(0)=⋯=un-1(0)=0,u(1)+pu′(1)=qu′(ξ), where cD0+ρis the Caputo fractional derivative of orderρ, and the functionf:[0,1]×[0,∞)↦[0,+∞)is continuously differentiable. Here,0⩽q⩽p,0<ξ<1,2⩽n-1<ρ<n. By virtue of some fixed point theorems, some sufficient criteria for the existence and multiplicity results of positive solutions are established and the obtained results also guarantee that the positive solutions discussed are monotone and concave.

scholarly journals Existence of Positive Solutions for Two-Point Boundary Value Problems of Nonlinear Finite Discrete Fractional Differential Equations and Its Application

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Caixia Guo ◽  
Jianmin Guo ◽  
Ying Gao ◽  
Shugui Kang
Keyword(s):  
Green Function ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Point Boundary ◽  
Fractional Differential ◽  
The Green Function

This paper is concerned with the two-point boundary value problems of nonlinear finite discrete fractional differential equations. On one hand, we discuss some new properties of the Green function. On the other hand, by using the main properties of Green function and the Krasnoselskii fixed point theorem on cones, some sufficient conditions for the existence of at least one or two positive solutions for the boundary value problem are established.

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