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.

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.

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 and Monotone Iteration of Positive Pseudosymmetric Solutions for a Third-Order Four-Point BVP

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Xuezhe Lv ◽  
Libo Wang ◽  
Minghe Pei
Keyword(s):  
Boundary Value Problem ◽  
Existence Result ◽  
Iterative Scheme ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Point Boundary ◽  
Third Order ◽  
Monotone Iteration ◽  
Monotone Iterative ◽  
Order Four

We study the existence and monotone iteration of solutions for a third-order four-point boundary value problem. An existence result of positive, concave, and pseudosymmetric solutions and its monotone iterative scheme are established by using the monotone iterative technique. Meanwhile, as an application of our results, an example is given.

Monotone Iterative Technique for Periodic Boundary Value Problem of Fractional Differential Equation in Banach Spaces

2019 ◽  
Vol 20 (5) ◽  
pp. 595-599 ◽  
Author(s):  
Pengyu Chen ◽  
Yibo Kong
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Banach Spaces ◽  
Fractional Differential Equation ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Monotone Iterative ◽  
Fractional Differential

AbstractIn this paper, we are concerned with the periodic boundary value problem of fractional differential equations on ordered Banach spaces. By introducing a concept of upper and lower solutions, we construct a new monotone iterative technique for the periodic boundary value problems of fractional differential equation, and obtain the existence of solutions between lower and upper solutions.

scholarly journals Existence and Monotone Iteration of Positive Pseudosymmetric Solutions for a Third-Order Four-Point BVP with -Laplacian

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Dan Li ◽  
Libo Wang ◽  
Minghe Pei
Keyword(s):  
Boundary Value Problem ◽  
Existence Result ◽  
Iterative Scheme ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Point Boundary ◽  
Third Order ◽  
Monotone Iteration ◽  
Monotone Iterative ◽  
Order Four

We study the existence and monotone iteration of solutions for a third-order four-point boundary value problem with -Laplacian. An existence result of positive, concave, and pseudosymmetric solutions and its monotone iterative scheme are established by using the monotone iterative technique. Meanwhile, as an application of our result, an example is given.

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