scholarly journals Existence of triple positive solutions for a third-order three-point boundary value problem

2008 ◽  
Vol 221 (1) ◽  
pp. 194-201 ◽  
Author(s):  
Yongping Sun
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Triple Positive Solutions

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 Triple Positive Solutions for Third-Orderm-Point Boundary Value Problems on Time Scales

2009 ◽  
Vol 2009 ◽  
pp. 1-15
Author(s):  
Jian Liu ◽  
Fuyi Xu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Triple Positive Solutions

We study the following third-orderm-point boundary value problems on time scales(φ(uΔ∇))∇+a(t)f(u(t))=0,t∈[0,T]T,u(0)=∑i=1m−2biu(ξi),uΔ(T)=0,φ(uΔ∇(0))=∑i=1m−2ciφ(uΔ∇(ξi)), whereφ:R→Ris an increasing homeomorphism and homomorphism andφ(0)=0,0<ξ1<⋯<ξm−2<ρ(T). We obtain the existence of three positive solutions by using fixed-point theorem in cones. The conclusions in this paper essentially extend and improve the known results.

scholarly journals Twin Positive Solutions of a Nonlinearm-Point Boundary Value Problem for Third-Orderp-Laplacian Dynamic Equations on Time Scales

2008 ◽  
Vol 2008 ◽  
pp. 1-19
Author(s):  
Wei Han ◽  
Guang Zhang
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Time Scales ◽  
Existence Theorems ◽  
Boundary Value ◽  
Dynamic Equations ◽  
Point Boundary ◽  
Third Order ◽  
Related Literature

Several existence theorems of twin positive solutions are established for a nonlinearm-point boundary value problem of third-orderp-Laplacian dynamic equations on time scales by using a fixed point theorem. We present two theorems and four corollaries which generalize the results of related literature. As an application, an example to demonstrate our results is given. The obtained conditions are different from some known results.

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