scholarly journals Existence of Positive Solution to System of Nonlinear Third-Order Three-Point BVPs

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Jian-Ping Sun ◽  
Xue-Mei Yang ◽  
Ya-Hong Zhao
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Main Tool ◽  
Point Boundary ◽  
Point Index ◽  
Third Order

We are concerned with the following system of third-order three-point boundary value problems:u′′′(t)+f(t,v(t))=0,t∈(0,1),v′′′(t)+g(t,u(t))=0,t∈(0,1),u(0)=u′′(0)=0,u′(1)=αu(η),v(0)=v′′(0)=0, andv′(1)=αv(η), where0<η<1and0<α<1/η. By imposing some suitable conditions onfandg, we obtain the existence of at least one positive solution to the above system. The main tool used is the theory of the fixed-point index.

Positive Solution of Nonlinear Two-Order Three-Point Boundary Value Problem for Difference Equation with Change of Sign

2014 ◽  
Vol 687-691 ◽  
pp. 1232-1236
Author(s):  
Chun Li Wang
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Point Boundary ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions

In this paper we investigate the existence of positive solution of the following discrete two-order three-point boundary value problemWherandis sign-changing on . By using the fixed-point index theory, the existence of positive solutions for the above boundary value problem is obtained.

Solutions of second order multi-point boundary value problems

2008 ◽  
Vol 145 (2) ◽  
pp. 489-510 ◽  
Author(s):  
JOHN R. GRAEF ◽  
LINGJU KONG
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problems ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
Nontrivial Solutions ◽  
Point Index ◽  
Linear Integral ◽  
The Relationship

AbstractWe consider classes of second order boundary value problems with a nonlinearity f(t, x) in the equations and subject to a multi-point boundary condition. Criteria are established for the existence of nontrivial solutions, positive solutions, and negative solutions of the problems under consideration. The symmetry of solutions is also studied. Conditions are determined by the relationship between the behavior of the quotient f(t, x)/x for x near 0 and ∞ and the largest positive eigenvalue of a related linear integral operator. Our analysis mainly relies on the topological degree and fixed point index theories.

scholarly journals Positive Solutions for a Class of Third-Order Three-Point Boundary Value Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Xiaojie Lin ◽  
Zhengmin Fu
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Positive Parameter ◽  
Point Boundary ◽  
Point Index ◽  
Third Order ◽  
Index Theorems ◽  
Existence Of Positive Solutions

We investigate the problem of existence of positive solutions for the nonlinear third-order three-point boundary value problemu‴(t)+λa(t)f(u(t))=0,0<t<1,u(0)=u′(0)=0,u″(1)=∝u″(η), whereλis a positive parameter,∝∈(0,1),η∈(0,1),f:(0,∞)→(0,∞),a:(0,1)→(0,∞)are continuous. Using a specially constructed cone, the fixed point index theorems and Leray-Schauder degree, this work shows the existence and multiplicities of positive solutions for the nonlinear third-order boundary value problem. Some examples are given to demonstrate the main results.

scholarly journals Positive solutions of three-point boundary value problems for higher-orderp-Laplacian with infinitely many singularities

2006 ◽  
Vol 2006 ◽  
pp. 1-12 ◽  
Author(s):  
Fuyi Xu ◽  
Yonghong Wu ◽  
Lishan Liu ◽  
Yunming Zhou
Keyword(s):  
Fixed Point ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Index Theorem ◽  
Point Boundary ◽  
Point Index ◽  
Fixed Point Index Theorem ◽  
Infinitely Many Singularities

We study a three-point nonlinear boundary value problem with higher-orderp-Laplacian. We show that there exist countable many positive solutions by using the fixed point index theorem for operators in a cone.

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