scholarly journals Positive Solutions for a Class of p-Laplacian Hadamard Fractional-Order Three-Point Boundary Value Problems

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 308 ◽  
Author(s):  
Jiafa Xu ◽  
Jiqiang Jiang ◽  
Donal O’Regan
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fractional Order ◽  
Boundary Value ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Point Boundary ◽  
Monotone Iterative ◽  
Existence Of Positive Solutions

In this paper, using the Avery–Henderson fixed point theorem and the monotone iterative technique, we investigate the existence of positive solutions for a class of p-Laplacian Hadamard fractional-order three-point boundary value problems.

scholarly journals Existence of Positive Solutions for Multi-Point Boundary Value Problems on Infinite Intervals in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Zhaocai Hao ◽  
Liang Ma
Keyword(s):  
Banach Spaces ◽  
Positive Solutions ◽  
Boundary Value ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Point Boundary ◽  
Monotone Iterative ◽  
Mönch Fixed Point Theorem ◽  
Existence Of Positive Solutions ◽  
Infinite Intervals

We investigate the positive solutions of a class of second-order nonlinear singular differential equations with multi-point boundary value conditions on an infinite interval in Banach spaces. The tools we used are the cone theory and Mönch fixed point theorem and a monotone iterative technique. An example is also given to demonstrate the applications of our results, which include and extend some existing results.

scholarly journals EXISTENCE OF POSITIVE SOLUTIONS FOR SUPERLINEAR SEMIPOSITONE $m$-POINT BOUNDARY-VALUE PROBLEMS

2003 ◽  
Vol 46 (2) ◽  
pp. 279-292 ◽  
Author(s):  
Ruyun Ma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Positive Parameter ◽  
Point Boundary ◽  
Existence Of Positive Solutions ◽  
The Fixed Point Theorem

AbstractIn this paper we consider the existence of positive solutions to the boundary-value problems\begin{align*} (p(t)u')'-q(t)u+\lambda f(t,u)\amp=0,\quad r\ltt\ltR, \\[2pt] au(r)-bp(r)u'(r)\amp=\sum^{m-2}_{i=1}\alpha_iu(\xi_i), \\ cu(R)+dp(R)u'(R)\amp=\sum^{m-2}_{i=1}\beta_iu(\xi_i), \end{align*}where $\lambda$ is a positive parameter, $a,b,c,d\in[0,\infty)$, $\xi_i\in(r,R)$, $\alpha_i,\beta_i\in[0,\infty)$ (for $i\in\{1,\dots m-2\}$) are given constants satisfying some suitable conditions. Our results extend some of the existing literature on superlinear semipositone problems. The proofs are based on the fixed-point theorem in cones.AMS 2000 Mathematics subject classification: Primary 34B10, 34B18, 34B15

scholarly journals Successive Iteration and Positive Solutions for Nonlinearm-Point Boundary Value Problems on Time Scales

2009 ◽  
Vol 2009 ◽  
pp. 1-13
Author(s):  
Yanbin Sang
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Time Scales ◽  
Boundary Value ◽  
Point Boundary ◽  
Iterative Schemes ◽  
Monotone Iterative ◽  
Successive Iteration ◽  
Existence Of Positive Solutions ◽  
Cone Expansion And Compression

We study the existence of positive solutions for a class ofm-point boundary value problems on time scales. Our approach is based on the monotone iterative technique and the cone expansion and compression fixed point theorem of norm type. Without the assumption of the existence of lower and upper solutions, we do not only obtain the existence of positive solutions of the problem, but also establish the iterative schemes for approximating the solutions.

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.

The Existence of Positive Solutions for Boundary Value Problems of Fractional Differential Equation

2014 ◽  
Vol 711 ◽  
pp. 303-307 ◽  
Author(s):  
Jie Gao
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Boundary Value ◽  
Point Boundary ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

In this paper, by using Leggett-Williams fixed point theorem, we will study the existence of positive solutions for a class of multi-point boundary value problems of fractional differential equation on infinite interval.

scholarly journals Existence Results and the Monotone Iterative Technique for Nonlinear Fractional Differential Systems with Coupled Four-Point Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Yujun Cui ◽  
Yumei Zou
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Point Boundary ◽  
Differential Systems ◽  
Monotone Iterative ◽  
Fractional Differential Systems ◽  
Fractional Differential

By establishing a comparison result and using the monotone iterative technique combined with the method of upper and lower solutions, we investigate the existence of solutions for nonlinear fractional differential systems with coupled four-point boundary value problems.

Symmetric positive solutions for the systems of higher-order boundary value problems on time scales

2017 ◽  
Vol 8 (4) ◽  
Author(s):  
Arzu Denk Oğuz ◽  
Fatma Serap Topal
Keyword(s):  
Boundary Value Problems ◽  
Recent Work ◽  
Positive Solutions ◽  
Time Scales ◽  
Boundary Value ◽  
Higher Order ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Monotone Iterative ◽  
Symmetric Positive Solutions

AbstractIn this paper, we discuss the existence of symmetric positive solutions for the systems of higher-order boundary value problems on time scales. Our results extend some recent work in the literature. The analysis of this paper mainly relies on the monotone iterative technique.

scholarly journals Positive Solutions for Third-Order Nonlinearp-Laplacianm-Point Boundary Value Problems on Time Scales

2008 ◽  
Vol 2008 ◽  
pp. 1-16 ◽  
Author(s):  
Fuyi Xu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Time Scales ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Point Boundary ◽  
Third Order ◽  
Existence Of Positive Solutions

We study the following third-orderp-Laplacianm-point boundary value problems on time scales:(ϕp(uΔ∇))∇+a(t)f(t,u(t))=0,t∈[0,T]T,βu(0)−γuΔ(0)=0,u(T)=∑i=1m−2aiu(ξi),ϕp(uΔ∇(0))=∑i=1m−2biϕp(uΔ∇(ξi)), whereϕp(s)isp-Laplacian operator, that is,ϕp(s)=|s|p−2s,p>1,  ϕp−1=ϕq,1/p+1/q=1,  0<ξ1<⋯<ξm−2<ρ(T). We obtain the existence of positive solutions by using fixed-point theorem in cones. The conclusions in this paper essentially extend and improve the known results.

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