Journal ArticleDOI
A monotone iterative technique for solving the bending elastic beam equations
TLDR
Using this maximum principle, a monotone iterative technique in the presence of lower and upper solutions to solve the nonlinear equation and obtain some existence and uniqueness results.About:
This article is published in Applied Mathematics and Computation.The article was published on 2010-11-01. It has received 20 citations till now. The article focuses on the topics: Maximum principle & Boundary value problem.read more
Citations
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Journal ArticleDOI
Existence and iterative method for some fourth order nonlinear boundary value problems
TL;DR: By the use of a novel efficient method for nonlinear fourth order boundary value problem, the existence and uniqueness of solution for the problem is obtained and the monotony of iterations is considered.
Journal ArticleDOI
A novel efficient method for nonlinear boundary value problems
TL;DR: A novel efficient method for a fourth-order nonlinear boundary value problem which models a statistically bending elastic beam is proposed, which guarantees the existence and uniqueness of a solution of the problem and the convergence of an iterative method for finding it.
Journal ArticleDOI
Nonlinear large deflection problems of beams with gradient: A biparametric perturbation method
TL;DR: A new perturbation method with two small parameters, one describes the loads effect and another describes the geometrical nature of the problem, is used to solve the nonlinear large deflection problem of beams with gradient under the two different boundary conditions.
Journal ArticleDOI
Iterative method for a class of fourth-order p-Laplacian beam equation
TL;DR: In this article, the existence and uniqueness result of the boundary value problem for a class of fourth-order p-Laplacians was obtained. But the authors considered the boundary values problem in the case of an elastic beam, and they used a novel efficient iteration method.
Journal ArticleDOI
Monotone Iterative Technique for a Class of Slanted Cantilever Beam Equations
TL;DR: In this article, the existence and uniqueness of the solutions of the two-point boundary value problem of fourth-order ODEs with continuous function was studied, where the static deformation of an elastic beam whose left end-point is fixed and right is freed is described.
References
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Journal ArticleDOI
Existence and uniqueness theorems for fourth-order boundary value problems
TL;DR: In this article, the authors considered a more general problem, namely, y(4) = f ( x, y, y\") (1.1) whe re fe C[ [-0, 1 ] x R x R, R], under the following types of boundary conditions.
Journal ArticleDOI
On positive solutions of some nonlinear fourth-order beam equations
Zhanbing Bai,Haiyan Wang +1 more
TL;DR: In this article, the existence, uniqueness and multiplicity of positive solutions of the boundary value problem were studied. But the existence and uniqueness of the positive solutions were not investigated. And they were not considered for the case where λ > 0.
Journal ArticleDOI
The Method of Lower and Upper Solutions for Fourth-Order Two-Point Boundary Value Problems
Ma Ruyun,Zhang Jihui,Fu Shengmao +2 more
TL;DR: In this article, the monotone method was developed in the presence of lower and upper solutions for the problem u (IV) = f(x, u(x), u″(x)).
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