scholarly journals Existence and uniqueness of convex monotone positive solutions for boundary value problems of an elastic beam equation with a parameter

2015 ◽  
pp. 1-11 ◽  
Author(s):  
Chengbo Zhai ◽  
Chunrong Jiang
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Elastic Beam ◽  
Beam Equation ◽  
Elastic Beam Equation ◽  
Monotone Positive Solutions

scholarly journals Monotone Positive Solutions for an Elastic Beam Equation with Nonlinear Boundary Conditions

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Jian-Ping Sun ◽  
Xian-Qiang Wang
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Nonlinear Boundary ◽  
Quadratic Function ◽  
Elastic Beam ◽  
Nonlinear Boundary Conditions ◽  
Beam Equation ◽  
Iterative Schemes ◽  
Elastic Beam Equation ◽  
Monotone Positive Solutions

This paper is concerned with the existence of monotone positive solutions for an elastic beam equation with nonlinear boundary conditions. By applying monotone iteration method, we not only obtain the existence of monotone positive solutions but also establish iterative schemes for approximating the solutions. It is worth mentioning that these iterative schemes start off with zero function or quadratic function, which is very useful and feasible for computational purpose. An example is also included to illustrate the main results obtained.

scholarly journals New Results for Multipoint Singular Boundary Value Problems on a Measure Chain

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yan Sun ◽  
Yongping Sun ◽  
Patricia J. Y. Wong
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Singular Boundary ◽  
Sufficient Condition ◽  
Point Boundary ◽  
Singular Boundary Value Problems ◽  
Second Order Differential Equations ◽  
Maximal Principle

We study the existence and uniqueness of positive solutions for a class of singularm-point boundary value problems of second order differential equations on a measure chain. A sharper sufficient condition for the existence and uniqueness ofCrd⁡1[0,T]positive solutions as well asCrd⁡1[0,T]positive solutions is obtained by the technique of lower and upper solutions and the maximal principle theorem.

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