scholarly journals Monotone iterative technique and symmetric positive solutions for a fourth-order boundary value problem

2010 ◽  
Vol 51 (9-10) ◽  
pp. 1260-1267 ◽  
Author(s):  
Minghe Pei ◽  
Sung Kag Chang
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Boundary Value ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Monotone Iterative ◽  
Symmetric Positive Solutions

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.

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.

Unique positive solution for a fractional boundary value problem

2013 ◽  
Vol 16 (4) ◽  
Author(s):  
Keyu Zhang ◽  
Jiafa Xu
Keyword(s):  
Boundary Value Problem ◽  
Positive Solution ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Fractional Boundary Value Problem ◽  
Unique Positive Solution ◽  
Monotone Iterative ◽  
Liouville Fractional Derivative

AbstractIn this work we consider the unique positive solution for the following fractional boundary value problem $\left\{ \begin{gathered} D_{0 + }^\alpha u(t) = - f(t,u(t)),t \in [0,1], \hfill \\ u(0) = u'(0) = u'(1) = 0. \hfill \\ \end{gathered} \right. $ Here α ∈ (2, 3] is a real number, D 0+α is the standard Riemann-Liouville fractional derivative of order α. By using the method of upper and lower solutions and monotone iterative technique, we also obtain that there exists a sequence of iterations uniformly converges to the unique solution.

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 Theory for Positive Iterative Solutions to a Type of Boundary Value Problem

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1585
Author(s):  
Bo Sun
Keyword(s):  
Boundary Value Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Monotone Iterative Technique ◽  
Existence Theory ◽  
Iterative Technique ◽  
Third Order ◽  
Research Results ◽  
Monotone Iterative ◽  
Iterative Solutions

We introduce some research results on a type of third-order boundary value problem for positive iterative solutions. The existence of solutions to these problems was proved using the monotone iterative technique. As an examination of the proposed method, an example to illustrate the effectiveness of our results was presented.

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