Existence of Positive Solution for a Second Order two Point Boundary Value Problem with Sign-changing Green's Function

2012 ◽  
Vol 14 (2) ◽  
pp. 113
Author(s):  
Feng WANG ◽  
Xiangli FEI ◽  
Limin YAN
Keyword(s):  
Boundary Value Problem ◽  
Green’S Function ◽  
Positive Solution ◽  
Green's Function ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary

scholarly journals Iteration for a Third-Order Three-Point BVP with Sign-Changing Green's Function

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Ya-Hong Zhao ◽  
Xing-Long Li
Keyword(s):  
Iterative Method ◽  
Boundary Value Problem ◽  
Green’S Function ◽  
Positive Solution ◽  
Green's Function ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Monotone Positive Solution

We are concerned with the following third-order three-point boundary value problem:u‴(t)=f(t,u(t)),t∈[0,1],u′(0)=u(1)=0,u″(η)+αu(0)=0, whereα∈[0,2)andη∈[2/3,1). Although corresponding Green's function is sign-changing, we still obtain the existence of monotone positive solution under some suitable conditions onfby applying iterative method. An example is also included to illustrate the main results obtained.

scholarly journals Multiplicity of Positive Solutions for a Singular Second-Order Three-Point Boundary Value Problem with a Parameter

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Jian Liu ◽  
Hanying Feng ◽  
Xingfang Feng
Keyword(s):  
Boundary Value Problem ◽  
Green’S Function ◽  
Positive Solutions ◽  
Green's Function ◽  
Boundary Value ◽  
Index Theory ◽  
Second Order ◽  
Point Boundary ◽  
Fixed Point Index Theory ◽  
Multiplicity Of Positive Solutions

This paper is concerned with the following second-order three-point boundary value problemu″t+β2ut+λqtft,ut=0,t∈0 , 1,u0=0,u(1)=δu(η), whereβ∈(0,π/2),δ>0,η∈(0,1), andλis a positive parameter. First, Green’s function for the associated linear boundary value problem is constructed, and then some useful properties of Green’s function are obtained. Finally, existence, multiplicity, and nonexistence results for positive solutions are derived in terms of different values ofλby means of the fixed point index theory.

Existence of Positive Solutions of Nonlinear Second-Order M-Point Boundary Value Problem

2011 ◽  
Vol 2 (1) ◽  
pp. 28-33
Author(s):  
F. H. Wong ◽  
C. J. Chyan ◽  
S. W. Lin
Keyword(s):  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
Existence Of Positive Solutions

Under suitable conditions on, the nonlinear second-order m-point boundary value problem has at least one positive solution. In this paper, the authors examine the positive solutions of nonlinear second-order m-point boundary value problem.

A priori estimates of the positive solution of the two-point boundary value problem for one second-order nonlinear differential equation

2019 ◽  
pp. 38-48
Author(s):  
Edelkhan Abduragimov
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Nonlinear Differential Equation ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Second Order ◽  
Point Boundary ◽  
Priori Estimates

A priori estimates of the positive solution of the two-point boundary value problem are obtained $y^{\prime\prime}=-f(x,y)$, $0<x<1$, $y(0)=y(1)=0$ assuming that $f(x,y)$ is continuous at $x \in [0,1]$, $y \in R$ and satisfies the condition $a_0 x^{\gamma}y^p \leq f(x,y) \leq a_1 y^p$, where $a_0>0$, $a_1>0$, $p>1$, $\gamma \geq 0$ -- constants.

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