scholarly journals Discrete First-Order Three-Point Boundary Value Problem

2009 ◽  
Vol 1 (2) ◽  
Author(s):  
M. Mohamed ◽  
H. B. Thompson ◽  
M. S. Jusoh ◽  
K. Jusoff
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Point Boundary ◽  
First Order

scholarly journals Positive Solutions for Nonlinear First-Orderm-Point Boundary Value Problem on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
İsmail Yaslan
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Time Scales ◽  
Time Scale ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Point Boundary ◽  
First Order ◽  
Existence Of Positive Solutions

By means of fixed-point theorems, we investigate the existence of positive solutions for nonlinear first-order -point boundary value problem , , where is a time scale, , are given constants.

scholarly journals On third-order three-point right focal boundary value problems

2008 ◽  
Vol 39 (4) ◽  
pp. 317-324
Author(s):  
Xiangyun Wu ◽  
Zhanbing Bai
Keyword(s):  
Fixed Point ◽  
Continuous Function ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
First Order ◽  
Existence Of Positive Solutions ◽  
Nonnegative Continuous Function

In this paper, a fixed point theorem in a cone, some inequalities of the associated Green's function and the concavity of solutions are applied to obtain the existence of positive solutions of third-order three-point boundary value problem with dependence on the first-order derivative$\begin{cases}& x'''(t) = f(t, x(t), x'(t)), \quad 0 < t < 1, \\ & x(0) = x'(\eta) = x''(1) = 0, \end{cases}$where $f:[0, 1]\times[0, \infty)\times R\to [0,\infty)$ is a nonnegative continuous function, $\eta\in(1/2, 1).$

scholarly journals Existence of Multiple Positive Solutions for Even Order Multi-Point Boundary Value Problems

2007 ◽  
Vol 14 (4) ◽  
pp. 775-792
Author(s):  
Youyu Wang ◽  
Weigao Ge
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Multiple Positive Solutions ◽  
Point Boundary ◽  
Even Order

Abstract In this paper, we consider the existence of multiple positive solutions for the 2𝑛th order 𝑚-point boundary value problem: where (0,1), 0 < ξ 1 < ξ 2 < ⋯ < ξ 𝑚–2 < 1. Using the Leggett–Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The associated Green's function for the above problem is also given.

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