scholarly journals Multiple Positive Solutions to Multipoint Boundary Value Problem for a System of Second-Order Nonlinear Semipositone Differential Equations on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Gang Wu ◽  
Longsuo Li ◽  
Xinrong Cong ◽  
Xiufeng Miao
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Time Scales ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Second Order ◽  
Dynamic Equations ◽  
Multiple Positive Solutions ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problem

We study a system of second-order dynamic equations on time scales(p1u1∇)Δ(t)-q1(t)u1(t)+λf1(t,u1(t),u2(t))=0,t∈(t1,tn),(p2u2∇)Δ(t)-q2(t)u2(t)+λf2(t,u1(t),u2(t))=0, satisfying four kinds of different multipoint boundary value conditions,fiis continuous and semipositone. We derive an interval ofλsuch that anyλlying in this interval, the semipositone coupled boundary value problem has multiple positive solutions. The arguments are based upon fixed-point theorems in a cone.

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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