Existence of Positive Solutions for a Class of Sigular Boundary Value Problem of Fourth Order

2004 ◽  
Vol 20 (4) ◽  
pp. 665-674 ◽  
Author(s):  
Ming Xiong
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Boundary Value ◽  
Existence Of Positive Solutions

scholarly journals Positive Solutions for Two-Point Boundary Value Problems for Fourth-Order Differential Equations with Fully Nonlinear Terms

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yixin Zhang ◽  
Yujun Cui
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Linear Operators ◽  
Continuous Space ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions

In this paper, we consider the existence of positive solutions for the fully fourth-order boundary value problem u 4 t = f t , u t , u ′ t , u ″ t , u ‴ t ,   0 ≤ t ≤ 1 , u 0 = u 1 = u ″ 0 = u ″ 1 = 0 , where f : 0,1 × 0 , + ∞ × − ∞ , + ∞ × − ∞ , 0 × − ∞ , + ∞ ⟶ 0 , + ∞ is continuous. This equation can simulate the deformation of an elastic beam simply supported at both ends in a balanced state. By using the fixed-point index theory and the cone theory, we discuss the existence of positive solutions of the fully fourth-order boundary value problem. We transform the fourth-order differential equation into a second-order differential equation by order reduction method. And then, we examine the spectral radius of linear operators and the equivalent norm on continuous space. After that, we obtain the existence of positive solutions of such BVP.

scholarly journals Existence of Positive Solutions for a Fourth-Order Periodic Boundary Value Problem

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Yongxiang Li
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Fixed Point Index ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Index Theory ◽  
Periodic Boundary Value Problem ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions

The existence results of positive solutions are obtained for the fourth-order periodic boundary value problemu(4)−βu′′+αu=f(t,u,u′′),0≤t≤1,u(i)(0)=u(i)(1),  i=0,1,2,3, wheref:[0,1]×R+×R→R+is continuous,α,β∈R,and satisfy0<α<((β/2)+2π2)2,β>−2π2,(α/π4)+(β/π2)+1>0. The discussion is based on the fixed point index theory in cones.

scholarly journals Positive Solutions of a Nonlinear Fourth-order Integral Boundary Value Problem

2016 ◽  
Vol 54 (1) ◽  
pp. 73-86 ◽  
Author(s):  
Slimane Benaicha ◽  
Faouzi Haddouchi
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Integral Condition ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Integral Boundary Value Problem ◽  
Existence Of Positive Solutions

Abstract In this paper, the existence of positive solutions for a nonlinear fourth-order two-point boundary value problem with integral condition is investigated. By using Krasnoselskii’s fixed point theorem on cones, sufficient conditions for the existence of at least one positive solutions are obtained.

Sign in / Sign up

Export Citation Format

Share Document