scholarly journals Positive Solutions for a Three-Point Boundary Value Problem of Fractional Q-Difference Equations

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 358 ◽  
Author(s):  
Chen Yang
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Difference Equations ◽  
Fixed Point Theorems ◽  
Iterative Scheme ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Monotone Operators ◽  
Point Boundary ◽  
Mixed Monotone Operators

In this work, a three-point boundary value problem of fractional q-difference equations is discussed. By using fixed point theorems on mixed monotone operators, some sufficient conditions that guarantee the existence and uniqueness of positive solutions are given. In addition, an iterative scheme can be made to approximate the unique solution. Finally, some interesting examples are provided to illustrate the main results.

scholarly journals Positive Solutions to a Fractional-Order Two-Point Boundary Value Problem with p-Laplacian Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Xiangshan Kong ◽  
Haitao Li
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Operator Equation ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Laplacian Operator ◽  
Point Boundary ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions

This paper systematically investigates positive solutions to a kind of two-point boundary value problem (BVP) for nonlinear fractional differential equations with p-Laplacian operator and presents a number of new results. First, the considered BVP is converted to an operator equation by using the property of the Caputo derivative. Second, based on the operator equation and some fixed point theorems, several sufficient conditions are presented for the nonexistence, the uniqueness, and the multiplicity of positive solutions. Finally, several illustrative examples are given to support the obtained new results. The study of illustrative examples shows that the obtained results are effective.

scholarly journals Existence of Multiple Positive Solutions for Even Order Multi-Point Boundary Value Problems

2007 ◽  
Vol 14 (4) ◽  
pp. 775-792
Author(s):  
Youyu Wang ◽  
Weigao Ge
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Multiple Positive Solutions ◽  
Point Boundary ◽  
Even Order

Abstract In this paper, we consider the existence of multiple positive solutions for the 2𝑛th order 𝑚-point boundary value problem: where (0,1), 0 < ξ 1 < ξ 2 < ⋯ < ξ 𝑚–2 < 1. Using the Leggett–Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The associated Green's function for the above problem is also given.

scholarly journals Multiple Positive Solutions of a Second Order Nonlinear Semipositonem-Point Boundary Value Problem on Time Scales

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Chengjun Yuan ◽  
Yongming Liu
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Time Scales ◽  
Dynamic Equation ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Second Order ◽  
Multiple Positive Solutions ◽  
Point Boundary

In this paper, we study a general second-orderm-point boundary value problem for nonlinear singular dynamic equation on time scalesuΔ∇(t)+a(t)uΔ(t)+b(t)u(t)+λq(t)f(t,u(t))=0,t∈(0,1)&#x1D54B;,u(ρ(0))=0,u(σ(1))=∑i=1m-2αiu(ηi). This paper shows the existence of multiple positive solutions iffis semipositone and superlinear. The arguments are based upon fixed-point theorems in a cone.

Existence of positive solutions for Riemann–Liouville fractional order three-point boundary value problem

2015 ◽  
Vol 08 (04) ◽  
pp. 1550057 ◽  
Author(s):  
Sabbavarapu Nageswara Rao
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fractional Order ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Point Boundary ◽  
Existence Of Positive Solutions

In this paper, we study the following fractional order three-point boundary value problem [Formula: see text] where [Formula: see text], are the standard Riemann–Liouville fractional order derivatives with [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]: [Formula: see text] is continuous. By using several well-known fixed-point theorems in a cone, the existence of at least one and two positive solutions is obtained. Some examples are presented to illustrate the main results.

scholarly journals Positive Solutions for Nonlinear First-Orderm-Point Boundary Value Problem on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
İsmail Yaslan
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Time Scales ◽  
Time Scale ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Point Boundary ◽  
First Order ◽  
Existence Of Positive Solutions

By means of fixed-point theorems, we investigate the existence of positive solutions for nonlinear first-order -point boundary value problem , , where is a time scale, , are given constants.

Some New Existence Results for a Class of Four Point Nonlinear Boundary Value Problems

2019 ◽  
Vol 3 (1) ◽  
Author(s):  
Nazia Urus ◽  
Amit K. Verma ◽  
Mandeep Singh
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Iterative Scheme ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Point Boundary ◽  
Nonlinear Boundary Value Problems ◽  
Monotone Iterative

In this paper we consider the following class of four point boundary value problems—y"(x) = f (x, y), 0 less than x lessthan 1, y'(0) = 0, y(1) = 1y(1) + 2)7(2)’where 1, 2  0 lesstahn 1, 2 less than 1, and f (x, y), is continuous in one sided Lipschitz in y. We propose a monotone iterative scheme and show that under some sufficient conditions this scheme generates sequences which converges uniformly to solution of the nonlinear multipint boundary value problem.

scholarly journals Positive Solutions for Three-Point Boundary Value Problem of Fractional Differential Equation with -Laplacian Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Shang-lin Yao ◽  
Guo-hui Wang ◽  
Zhi-ping Li ◽  
Li-jun Yu
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Laplacian Operator ◽  
Multiple Positive Solutions ◽  
Point Boundary ◽  
Fractional Differential

We investigate the existence of multiple positive solutions for three-point boundary value problem of fractional differential equation with -Laplacian operator , where are the standard Riemann-Liouville derivatives with , and the constant is a positive number satisfying ; -Laplacian operator is defined as . By applying monotone iterative technique, some sufficient conditions for the existence of multiple positive solutions are established; moreover iterative schemes for approximating these solutions are also obtained, which start off a known simple linear function. In the end, an example is worked out to illustrate our main results.

Existence of positive solutions for nonlocal boundary value problem of fractional differential equation

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Xiping Liu ◽  
Legang Lin ◽  
Haiqin Fang
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Nonlocal Boundary ◽  
Point Boundary ◽  
Nonlocal Boundary Value Problem ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

AbstractIn this paper, we study a type of nonlinear fractional differential equations multi-point boundary value problem with fractional derivative in the boundary conditions. By using the upper and lower solutions method and fixed point theorems, some results for the existence of positive solutions for the boundary value problem are established. Some examples are also given to illustrate our results.

Existence and nonexistence of positive solutions to a discrete boundary value problem

2017 ◽  
Vol 33 (2) ◽  
pp. 181-190
Author(s):  
JOHNNY HENDERSON ◽  
◽  
RODICA LUCA ◽  
ALEXANDRU TUDORACHE ◽  
◽  
...  
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Difference Equations ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
Order Difference ◽  
Discrete Boundary Value Problem ◽  
Existence And Nonexistence

We study the existence and nonexistence of positive solutions for a system of nonlinear second-order difference equations subject to coupled multi-point boundary conditions which contain some positive constants.

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