Existence of positive solutions for nonlinear third-order three-point boundary value problems

2008 ◽  
Vol 68 (10) ◽  
pp. 3151-3158 ◽  
Author(s):  
Li-Jun Guo ◽  
Jian-Ping Sun ◽  
Ya-Hong Zhao
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Existence Of Positive Solutions

scholarly journals Positive Solutions for Third-Order Nonlinearp-Laplacianm-Point Boundary Value Problems on Time Scales

2008 ◽  
Vol 2008 ◽  
pp. 1-16 ◽  
Author(s):  
Fuyi Xu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Time Scales ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Point Boundary ◽  
Third Order ◽  
Existence Of Positive Solutions

We study the following third-orderp-Laplacianm-point boundary value problems on time scales:(ϕp(uΔ∇))∇+a(t)f(t,u(t))=0,t∈[0,T]T,βu(0)−γuΔ(0)=0,u(T)=∑i=1m−2aiu(ξi),ϕp(uΔ∇(0))=∑i=1m−2biϕp(uΔ∇(ξi)), whereϕp(s)isp-Laplacian operator, that is,ϕp(s)=|s|p−2s,p>1,  ϕp−1=ϕq,1/p+1/q=1,  0<ξ1<⋯<ξm−2<ρ(T). We obtain the existence of positive solutions by using fixed-point theorem in cones. The conclusions in this paper essentially extend and improve the known results.

scholarly journals Existence of positive solutions for nonlinear third-order m-point boundary value problems on time scales

Filomat ◽  
2014 ◽  
Vol 28 (5) ◽  
pp. 925-935
Author(s):  
Ilkay Karacaa ◽  
Fatma Tokmaka
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Time Scales ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Growth Conditions ◽  
Point Boundary ◽  
Double Positive ◽  
Third Order ◽  
Existence Of Positive Solutions

In this paper, we investigate the existence of double positive solutions for nonlinear third-order m-point boundary value problems with p-Laplacian on time scales. By using double fixed point theorem, we establish results on the existence of two positive solutions with suitable growth conditions imposed on the nonlinear term. As an application, we give an example to demonstrate our main result.

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.

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