scholarly journals Unbounded Solutions of Second-Order Multipoint Boundary Value Problem on the Half-Line

2010 ◽  
Vol 2010 (1) ◽  
pp. 236560 ◽  
Author(s):  
Lishan Liu ◽  
Xinan Hao ◽  
Yonghong Wu
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Second Order ◽  
Half Line ◽  
Unbounded Solutions ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problem

scholarly journals Multiple Positive Solutions to Multipoint Boundary Value Problem for a System of Second-Order Nonlinear Semipositone Differential Equations on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Gang Wu ◽  
Longsuo Li ◽  
Xinrong Cong ◽  
Xiufeng Miao
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Time Scales ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Second Order ◽  
Dynamic Equations ◽  
Multiple Positive Solutions ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problem

We study a system of second-order dynamic equations on time scales(p1u1∇)Δ(t)-q1(t)u1(t)+λf1(t,u1(t),u2(t))=0,t∈(t1,tn),(p2u2∇)Δ(t)-q2(t)u2(t)+λf2(t,u1(t),u2(t))=0, satisfying four kinds of different multipoint boundary value conditions,fiis continuous and semipositone. We derive an interval ofλsuch that anyλlying in this interval, the semipositone coupled boundary value problem has multiple positive solutions. The arguments are based upon fixed-point theorems in a cone.

scholarly journals On a Singular Second-Order Multipoint Boundary Value Problem at Resonance

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
S. A. Iyase ◽  
O. F. Imaga
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Existence Results ◽  
Second Order ◽  
Multipoint Boundary ◽  
At Resonance ◽  
Problem At Resonance ◽  
Multipoint Boundary Value Problem

The aim of this paper is to derive existence results for a second-order singular multipoint boundary value problem at resonance using coincidence degree arguments.

scholarly journals Positive Solutions for Resonant and Nonresonant Nonlinear Third-Order Multipoint Boundary Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Liu Yang ◽  
Chunfang Shen ◽  
Dapeng Xie
Keyword(s):  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Boundary Value ◽  
Type Theorem ◽  
Third Order ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problems ◽  
First Time ◽  
Multipoint Boundary Value Problem

Positive solutions for a kind of third-order multipoint boundary value problem under the nonresonant conditions and the resonant conditions are considered. In the nonresonant case, by using the Leggett-Williams fixed point theorem, the existence of at least three positive solutions is obtained. In the resonant case, by using the Leggett-Williams norm-type theorem due to O’Regan and Zima, the existence result of at least one positive solution is established. It is remarkable to point out that it is the first time that the positive solution is considered for the third-order boundary value problem at resonance. Some examples are given to demonstrate the main results of the paper.

scholarly journals Global Structure of Positive Solutions for Some Second-Order Multipoint Boundary Value Problems

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Hongyu Li ◽  
Junting Zhang
Keyword(s):  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Boundary Value ◽  
Global Bifurcation ◽  
Global Structure ◽  
Second Order ◽  
Bifurcation Method ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problems

We investigate in this paper the following second-order multipoint boundary value problem:-(Lφ)(t)=λf(t,φ(t)),0≤t≤1,φ′0=0,φ1=∑i=1m-2βiφηi. Under some conditions, we obtain global structure of positive solution set of this boundary value problem and the behavior of positive solutions with respect to parameterλby using global bifurcation method. We also obtain the infinite interval of parameterλabout the existence of positive solution.

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