scholarly journals An even-order three-point boundary value problem on time scales

2004 ◽  
Vol 291 (2) ◽  
pp. 514-525 ◽  
Author(s):  
Douglas R Anderson ◽  
Richard I Avery
Keyword(s):  
Boundary Value Problem ◽  
Time Scales ◽  
Boundary Value ◽  
Point Boundary ◽  
Even Order

scholarly journals Existence of Multiple Positive Solutions for Even Order Multi-Point Boundary Value Problems

2007 ◽  
Vol 14 (4) ◽  
pp. 775-792
Author(s):  
Youyu Wang ◽  
Weigao Ge
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Multiple Positive Solutions ◽  
Point Boundary ◽  
Even Order

Abstract In this paper, we consider the existence of multiple positive solutions for the 2𝑛th order 𝑚-point boundary value problem: where (0,1), 0 < ξ 1 < ξ 2 < ⋯ < ξ 𝑚–2 < 1. Using the Leggett–Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The associated Green's function for the above problem is also given.

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 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)&#x1D54B;,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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