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.

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.

scholarly journals A NOTE ON EXISTENCE RESULTS FOR A CLASS OF THREE-POINT NONLINEAR BVPS

2015 ◽  
Vol 20 (4) ◽  
pp. 457-470 ◽  
Author(s):  
Amit K. Verma ◽  
Mandeep Singh
Keyword(s):  
Boundary Value Problem ◽  
Present Method ◽  
Iterative Scheme ◽  
Existence Results ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Point Boundary ◽  
Monotone Iterative ◽  
Close Form ◽  
User Friendly

This article deals with a computational iterative technique for the following second order three point boundary value problem y''(t) + f(t, y, y' ) = 0, 0 < t < 1, y(0) = 0, y(1) = δy(η), where f(I × R, R), I = [0, 1], 0 < η < 1, δ > 0. We consider simple iterative scheme and develop a monotone iterative technique. Some examples are constructed to show the accuracy of the present method. We show that our technique is quite powerful and some user friendly packages can be developed by using this technique to compute the solutions of the nonlinear three point BVPs whose close form solutions are not known.

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 Solvability of a nonlinear general third order four point eigenvalue problem on time scales

2011 ◽  
Vol 20 (2) ◽  
pp. 171-182
Author(s):  
S. NAGESWARA RAO ◽  
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Time Scales ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Order Four

We consider the four point boundary value problem for third order nonlinear differential equation on time scales ... subject to the boundary conditions ... t1 ≤ t2 ≤ t3 ≤ σ 3 (t4), α > 0, β > 0. Values of the parameter λ are determined for which the boundary value problem has a positive solution by utilizing a fixed point theorem on cone.

scholarly journals A remark on a third-order three-point boundary value problem

1994 ◽  
Vol 49 (1) ◽  
pp. 1-5 ◽  
Author(s):  
Salvatore A. Marano
Keyword(s):  
Boundary Value Problem ◽  
Real Function ◽  
Existence Result ◽  
Boundary Value ◽  
Pointwise Estimate ◽  
Continuation Theorem ◽  
Point Boundary ◽  
Third Order ◽  
Nonlinear Anal ◽  
Image Position

Let f be a real function defined on [0, 1] × R3 and let η ∈ (0, 1). Very recently, C.P. Gupta and V. Lakshimikantham, making use of the Leray-Schauder continuation theorem and Wirtinger-type inequalities, established an existence result for the problem(Theorem 1 and Remark 4 of [Nonlinear Anal. 16 (1991), 949–957]).The aim of the present paper is simply to point out how, bu means of a completely different approach, it is possible to improve that result not only by requiring much general on f, but also by giving a precise pointwise estimate on x″′

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