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

2008 ◽  
Vol 56 (9) ◽  
pp. 2429-2443 ◽  
Author(s):  
Douglas R. Anderson ◽  
Ilkay Yaslan Karaca
Keyword(s):  
Boundary Value Problem ◽  
Time Scales ◽  
Boundary Value ◽  
Higher Order ◽  
Point Boundary

scholarly journals Solvability of a Higher-Order Three-Point Boundary Value Problem on Time Scales

2009 ◽  
Vol 2009 ◽  
pp. 1-16 ◽  
Author(s):  
Yanbin Sang
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Time Scales ◽  
Existence Result ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Growth Conditions ◽  
Higher Order ◽  
Point Boundary ◽  
Nonlinear Alternative

We consider a higher-order three-point boundary value problem on time scales. A new existence result is first obtained by using a fixed point theorem due to Krasnoselskii and Zabreiko. Later, under certain growth conditions imposed on the nonlinearity, several sufficient conditions for the existence of a nonnegative and nontrivial solution are obtained by using Leray-Schauder nonlinear alternative. Our conditions imposed on nonlinearity are all very easy to verify; as an application, some examples to demonstrate our results are 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 Solutions of a multi-point boundary value problem for higher-order differential equations at resonance (III)

2005 ◽  
Vol 36 (2) ◽  
pp. 119-130 ◽  
Author(s):  
Yuji Liu ◽  
Weigao Ge
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Higher Order ◽  
Point Boundary ◽  
At Resonance ◽  
Higher Order Differential Equations

In this paper, we are concerned with the existence of solutions of the following multi-point boundary value problem consisting of the higher-order differential equations$ x^{(n)}(t)=f(t,x(t),x'(t),\cdots,x^{(n-1)}(t))+e(t),\;\;0

Sign in / Sign up

Export Citation Format

Share Document