scholarly journals Iterative Method for Solving a Beam Equation with Nonlinear Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Quang A. Dang ◽  
Nguyen Thanh Huong
Keyword(s):  
Iterative Method ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Order Equation ◽  
Beam Equation ◽  
Linear Boundary ◽  
Order Problem ◽  
Fourth Order Problem

In this paper, we propose an iterative method for solving a beam problem which is described by a nonlinear fourth-order equation with nonlinear boundary conditions. The method reduces this nonlinear fourth-order problem to a sequence of linear second-order problems with linear boundary conditions. The convergence of the method is proved, and some numerical examples demonstrate the efficiency of the method.

scholarly journals Multiple solutions for a fourth order equation with nonlinear boundary conditions: theoretical and numerical aspects

2019 ◽  
pp. 335-348
Author(s):  
Cristiane Aparecida Pendeza Martinez ◽  
André Luís Machado Martinez ◽  
Glaucia Maria Bressan ◽  
Emerson Vitor Castelani ◽  
Roberto Molina de Souza
Keyword(s):  
Boundary Conditions ◽  
Fourth Order ◽  
Multiple Solutions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Order Equation ◽  
Fourth Order Equation

scholarly journals Positive Solutions for a Singular Superlinear Fourth-Order Equation with Nonlinear Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Dongliang Yan
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Fourth Order ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Order Equation ◽  
Positive Parameter ◽  
Fourth Order Equation ◽  
Existence Of Positive Solutions ◽  
Small Positive Parameter

We show the existence of positive solutions for a singular superlinear fourth-order equation with nonlinear boundary conditions. u⁗x=λhxfux, x∈0,1,u0=u′0=0,u″1=0, u⁗1+cu1u1=0, where λ > 0 is a small positive parameter, f:0,∞⟶ℝ is continuous, superlinear at ∞, and is allowed to be singular at 0, and h: [0, 1] ⟶ [0, ∞) is continuous. Our approach is based on the fixed-point result of Krasnoselskii type in a Banach space.

Sign in / Sign up

Export Citation Format

Share Document