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 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 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 Picard Type Iterative Scheme with Initial Iterates in Reverse Order for a Class of Nonlinear Three Point BVPs

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Mandeep Singh ◽  
Amit K. Verma
Keyword(s):  
Source Term ◽  
Iterative Scheme ◽  
Upper And Lower Solutions ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Monotone Iterative Technique ◽  
Reverse Order ◽  
Monotone Iterative Method ◽  
Iterative Technique ◽  
Monotone Iterative

We consider the following class of three point boundary value problemy′′(t)+f(t,y)=0,0<t<1,y′(0)=0,y(1)=δy(η), whereδ>0,0<η<1, the source termf(t,y)is Lipschitz and continuous. We use monotone iterative technique in the presence of upper and lower solutions for both well-order and reverse order cases. Under some sufficient conditions, we prove some new existence results. We use examples and figures to demonstrate that monotone iterative method can efficiently be used for computation of solutions of nonlinear BVPs.

Some New Existence Results for a Class of Four Point Nonlinear Boundary Value Problems

2019 ◽  
Vol 3 (1) ◽  
Author(s):  
Nazia Urus ◽  
Amit K. Verma ◽  
Mandeep Singh
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Iterative Scheme ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Point Boundary ◽  
Nonlinear Boundary Value Problems ◽  
Monotone Iterative

In this paper we consider the following class of four point boundary value problems—y"(x) = f (x, y), 0 less than x lessthan 1, y'(0) = 0, y(1) = 1y(1) + 2)7(2)’where 1, 2  0 lesstahn 1, 2 less than 1, and f (x, y), is continuous in one sided Lipschitz in y. We propose a monotone iterative scheme and show that under some sufficient conditions this scheme generates sequences which converges uniformly to solution of the nonlinear multipint boundary value problem.

Ordinary Differential Equations with Nonlinear Boundary Conditions

2002 ◽  
Vol 9 (2) ◽  
pp. 287-294
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Monotone Iterative Technique ◽  
Lower And Upper Solutions ◽  
Iterative Technique ◽  
Monotone Iterative

Abstract The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems.

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.

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