scholarly journals Several Existence Theorems of Nonlinearm-Point BVP for an Increasing Homeomorphism and Homomorphism on Time Scales

2008 ◽  
Vol 2008 ◽  
pp. 1-13
Author(s):  
Yanbin Sang ◽  
Hua Su ◽  
Yafeng Xiao
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Time Scales ◽  
Existence Theorems ◽  
Boundary Value ◽  
Dynamic Equations ◽  
Point Boundary

Several existence theorems of positive solutions are established for nonlinearm-point boundary value problem for the following dynamic equations on time scales(ϕ(uΔ))∇+a(t)f(t,u(t))=0,t∈(0,T),ϕ(uΔ(0))=∑i=1m−2aiϕ(uΔ(ξi)),u(T)=∑i=1m−2biu(ξi), whereϕ:R→Ris an increasing homeomorphism and homomorphism andϕ(0)=0. As an application, an example to demonstrate our results is given.

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.

scholarly journals Multiple Positive Solutions of a Second Order Nonlinear Semipositonem-Point Boundary Value Problem on Time Scales

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Chengjun Yuan ◽  
Yongming Liu
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Time Scales ◽  
Dynamic Equation ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Second Order ◽  
Multiple Positive Solutions ◽  
Point Boundary

In this paper, we study a general second-orderm-point boundary value problem for nonlinear singular dynamic equation on time scalesuΔ∇(t)+a(t)uΔ(t)+b(t)u(t)+λq(t)f(t,u(t))=0,t∈(0,1)𝕋,u(ρ(0))=0,u(σ(1))=∑i=1m-2αiu(ηi). This paper shows the existence of multiple positive solutions iffis semipositone and superlinear. The arguments are based upon fixed-point theorems in a cone.

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