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 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 Computation of Positive Solutions for Nonlinear Impulsive Integral Boundary Value Problems withp-Laplacian on Infinite Intervals

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Xingqiu Zhang
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Monotone Iterative Technique ◽  
Second Order ◽  
Iterative Technique ◽  
Integral Boundary ◽  
Monotone Iterative ◽  
Infinite Intervals ◽  
Integral Boundary Value Problems

This paper deals with the existence and iteration of positive solutions for nonlinear second-order impulsive integral boundary value problems withp-Laplacian on infinite intervals. Our approach is based on the monotone iterative technique.

scholarly journals Monotone Iterative Technique and Symmetric Positive Solutions to Fourth-Order Boundary Value Problem with Integral Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Huihui Pang ◽  
Chen Cai
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Integral Boundary ◽  
Monotone Iterative ◽  
Symmetric Positive Solutions

The purpose of this paper is to investigate the existence of symmetric positive solutions for a class of fourth-order boundary value problem:u4(t)+βu′′(t)=f(t,u(t),u′′(t)),0<t<1,u(0)=u(1)=∫01‍p(s)u(s)ds,u′′(0)=u′′(1)=∫01‍qsu′′(s)ds, wherep,q∈L1[0,1],f∈C([0,1]×[0,∞)×(-∞,0],[0,∞)). By using a monotone iterative technique, we prove that the above boundary value problem has symmetric positive solutions under certain conditions. In particular, these solutions are obtained via the iteration procedures.

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.

scholarly journals Monotone iterative method for a class of nonlinear fractional differential equations on unbounded domains in Banach spaces

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1331-1338 ◽  
Author(s):  
Lihong Zhang ◽  
Bashir Ahmad ◽  
Guotao Wang
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Nonnegative Solution ◽  
Unbounded Domains ◽  
Monotone Iterative Technique ◽  
Monotone Iterative Method ◽  
Iterative Technique ◽  
Monotone Iterative ◽  
Fractional Differential ◽  
Infinite Intervals

In this paper, we investigate the existence of minimal nonnegative solution for a class of nonlinear fractional integro-differential equations on semi-infinite intervals in Banach spaces by applying the cone theory and the monotone iterative technique. An example is given for the illustration of main results.

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