scholarly journals Existence results for a boundary value problem involving a fourth-order elastic beam equation

2019 ◽  
Vol 2019 (1) ◽  
Keyword(s):  
Boundary Value Problem ◽  
Fourth Order ◽  
Boundary Value ◽  
Elastic Beam ◽  
Existence Results ◽  
Beam Equation ◽  
Elastic Beam Equation

scholarly journals Existence and Iteration of Monotone Positive Solution of BVP for an Elastic Beam Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Jian-Ping Sun ◽  
Xian-Qiang Wang
Keyword(s):  
Boundary Value Problem ◽  
Positive Solution ◽  
Iterative Scheme ◽  
Boundary Value ◽  
Elastic Beam ◽  
Beam Equation ◽  
Elastic Beam Equation ◽  
Monotone Positive Solution ◽  
Zero Function ◽  
Computational Purpose

This paper is concerned with the existence of monotone positive solution of boundary value problem for an elastic beam equation. By applying iterative techniques, we not only obtain the existence of monotone positive solution but also establish iterative scheme for approximating the solution. It is worth mentioning that the iterative scheme starts off with zero function, which is very useful and feasible for computational purpose. An example is also included to illustrate the main results.

scholarly journals S-Shaped Connected Component for Nonlinear Fourth-Order Problem of Elastic Beam Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Jinxiang Wang ◽  
Ruyun Ma ◽  
Jin Wen
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Boundary Value ◽  
Elastic Beam ◽  
Connected Components ◽  
Beam Equation ◽  
Connected Component ◽  
Order Problem ◽  
Fourth Order Problem

We investigate the existence of S-shaped connected component in the set of positive solutions of the fourth-order boundary value problem: u′′′′x=λhxfux, x∈(0,1),u(0)=u(1)=u′′0=u′′1=0, where λ>0 is a parameter, h∈C[0,1], and f∈C[0,∞) with f0≔lims→0⁡(f(s)/s)=∞. We develop a bifurcation approach to deal with this extreme situation by constructing a sequence of functions f[n] satisfying f[n]→f and (f[n])0→∞. By studying the auxiliary problems, we get a sequence of unbounded connected components C[n], and, then, we find an unbounded connected component C in the set of positive solutions of the fourth-order boundary value problem which satisfies 0,0∈C⊂lim⁡sup⁡C[n] and is S-shaped.

scholarly journals Existence Results for a Fully Fourth-Order Boundary Value Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yongxiang Li ◽  
Qiuyan Liang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Fourier Analysis ◽  
Growth Condition ◽  
Fourth Order ◽  
Boundary Value ◽  
Existence Of Solution ◽  
Existence Results ◽  
Analysis Method

We discuss the existence of solution for the fully fourth-order boundary value problemu(4)=f(t,u,u′,u′′,u′′′),0≤t≤1,u(0)=u(1)=u′′(0)=u′′(1)=0. A growth condition onfguaranteeing the existence of solution is presented. The discussion is based on the Fourier analysis method and Leray-Schauder fixed point theorem.

scholarly journals Solvability of a fourth order boundary value problem with periodic boundary conditions

1988 ◽  
Vol 11 (2) ◽  
pp. 275-284
Author(s):  
Chaitan P. Gupta
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Existence And Uniqueness ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Elastic Beam ◽  
Periodic Boundary Conditions ◽  
Uniqueness Of Solutions

Fourth order boundary value problems arise in the study of the equilibrium of an elastaic beam under an external load. The author earlier investigated the existence and uniqueness of the solutions of the nonlinear analogues of fourth order boundary value problems that arise in the equilibrium of an elastic beam depending on how the ends of the beam are supported. This paper concerns the existence and uniqueness of solutions of the fourth order boundary value problems with periodic boundary conditions.

Sign in / Sign up

Export Citation Format

Share Document