scholarly journals Global Behavior of the Components for the Second Order m-Point Boundary Value Problems

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
Yulian An ◽  
Ruyun Ma
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Global Behavior ◽  
Point Boundary

Positive solutions for singular second order three-point boundary value problems

2007 ◽  
Vol 66 (12) ◽  
pp. 2756-2766 ◽  
Author(s):  
Bingmei Liu ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary

scholarly journals Solvability of singular second order m-point boundary value problems of Dirichlet type

2005 ◽  
Vol 71 (1) ◽  
pp. 41-52 ◽  
Author(s):  
Ruyun Ma ◽  
Bevan Thompson
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Continuation Theorem ◽  
Point Boundary ◽  
Dirichlet Type ◽  
Carathéodory Conditions

Let f: [0, 1] × ℝ2 → ℝ be a function satisfying the Carathéodory conditions and t (1 − t) e (t) ∈ L1(0, 1). Let ai ∈ ℝ and ξi ∈ (0, 1) for i = 1, …, m − 2 where 0 < ξ1 < ξ2 < … < ξm−2 < 1. In this paper we study the existence of C[0, 1] solutions for the m-point boundary value problem The proof of our main result is based on the Leray-Schauder continuation theorem.

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