scholarly journals Multiple Positive Solutions for a System of Nonlinear Caputo-Type Fractional Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Hongyu Li ◽  
Yang Chen
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Fixed Point Index ◽  
Index Theory ◽  
Multiple Positive Solutions ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Fractional Differential

By using fixed-point index theory, we consider the existence of multiple positive solutions for a system of nonlinear Caputo-type fractional differential equations with the Riemann-Stieltjes boundary conditions.

scholarly journals Positive Solutions for a System of Hadamard-Type Fractional Differential Equations with Semipositone Nonlinearities

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Youzheng Ding ◽  
Jiqiang Jiang ◽  
Donal O’Regan ◽  
Jiafa Xu
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Fixed Point Index ◽  
Nonnegative Matrices ◽  
Point Index ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

In this paper, we use the fixed-point index and nonnegative matrices to study the existence of positive solutions for a system of Hadamard-type fractional differential equations with semipositone nonlinearities.

scholarly journals Multiplicity of Positive Solutions for Fractional Differential Equation withp-Laplacian Boundary Value Problems

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Sabbavarapu Nageswara Rao
Keyword(s):  
Fixed Point ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Index Theory ◽  
Laplacian Operator ◽  
Multiple Positive Solutions ◽  
Fixed Integer ◽  
Fixed Point Index Theory ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions

We investigate the existence of multiple positive solutions of fractional differential equations withp-Laplacian operatorDa+β(ϕp(Da+αu(t)))=f(t,u(t)),  a<t<b,uja=0,  j=0,1,2,…,n-2,u(α1)(b)=ξu(α1)(η),ϕp(Da+αu(a))=0=Da+β1(ϕp(Da+αu(b))), whereβ∈(1,2],α∈(n-1,n],  n≥3,ξ∈(0,∞),η∈(a,b),β1∈(0,1],α1∈{1,2,…,α-2}is a fixed integer, andϕp(s)=|s|p-2s,  p>1,  ϕp-1=ϕq,  (1/p)+(1/q)=1, by applying Leggett–Williams fixed point theorems and fixed point index theory.

scholarly journals Eigenvalue of Coupled Systems for Hammerstein Integral Equation with Two Parameters

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Wanjun Li
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Index Theory ◽  
Coupled Systems ◽  
Point Index ◽  
Hammerstein Integral Equation ◽  
Fixed Point Index Theory ◽  
Two Parameters

By using the fixed-point index theory, we discuss the existence, multiplicity, and nonexistence of positive solutions for the coupled systems of Hammerstein integral equation with parameters.

scholarly journals Positive Solutions for a Class of Fourth-Order Boundary Value Problems in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Jingjing Cai ◽  
Guilong Liu
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Positive Solutions ◽  
Fourth Order ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Existence And Nonexistence

Using a specially constructed cone and the fixed point index theory, this work shows existence and nonexistence results of positive solutions for fourth-order boundary value problem with two different parameters in Banach spaces.

scholarly journals Multiple positive solutions for a system of $(p_{1}, p_{2}, p_{3})$-Laplacian Hadamard fractional order BVP with parameters

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sabbavarapu Nageswara Rao ◽  
Abdullah Ali H. Ahmadini
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Laplacian Operator ◽  
Multiple Positive Solutions ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential

AbstractIn this article, we are pleased to investigate multiple positive solutions for a system of Hadamard fractional differential equations with $(p_{1}, p_{2}, p_{3})$ ( p 1 , p 2 , p 3 ) -Laplacian operator. The main results rely on the standard tools of different fixed point theorems. Finally, we demonstrate the application of the obtained results with the aid of examples.

scholarly journals On fixed point index theory for the sum of operators and applications to a class of ODEs and PDEs

2021 ◽  
Vol 22 (2) ◽  
pp. 259
Author(s):  
Svetlin Georgiev Georgiev ◽  
Karima Mebarki
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Point Index ◽  
Index Theory ◽  
Point Index ◽  
First Order ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions ◽  
Theoretical Results ◽  
Positive Half

The aim of this work is two fold: first  we  extend some results concerning the computation of the fixed point index for the sum of an expansive mapping and a $k$-set contraction  obtained in \cite{DjebaMeb, Svet-Meb}, to  the case of the sum $T+F$, where $T$ is a mapping such that $(I-T)$ is Lipschitz invertible and $F$ is a $k$-set contraction.  Secondly, as  illustration of some our theoretical results,  we study  the existence of positive solutions  for two classes of differential equations, covering a class of first-order ordinary differential equations (ODEs for short) posed on the positive half-line as well as  a class of  partial differential equations (PDEs for short).

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 On Six Solutions form-Point Differential Equations System with Two Coupled Parallel Sub-Super Solutions

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Jian Liu ◽  
Hua Su ◽  
Shuli Wang
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Point Index ◽  
Index Theory ◽  
Second Order ◽  
Point Index ◽  
Fixed Point Index Theory

Under the assumption of two coupled parallel subsuper solutions, the existence of at least six solutions for a kind of second-orderm-point differential equations system is obtained using the fixed point index theory. As an application, an example to demonstrate our result is given.

Positive Solutions for a Semipositone Singular Riemann–Liouville Fractional Differential Problem

2019 ◽  
Vol 20 (7-8) ◽  
pp. 823-831 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Rodica Luca
Keyword(s):  
Positive Solutions ◽  
Fractional Derivatives ◽  
Fixed Point Index ◽  
Index Theory ◽  
Multiple Positive Solutions ◽  
Differential Problem ◽  
Height Functions ◽  
Fixed Point Index Theory ◽  
Fractional Differential ◽  
Bounded Sets

AbstractWe study the existence of multiple positive solutions for a nonlinear singular Riemann–Liouville fractional differential equation with sign-changing nonlinearity, subject to Riemann–Stieltjes boundary conditions which contain fractional derivatives. In the proof of our main theorem, we use various height functions of the nonlinearity of equation defined on special bounded sets, and two theorems from the fixed point index theory.

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