Nonlinear triple-point problems on time scales

• Main Author: Douglas R. Anderson
• Format: Article
• Language: English
• Published: Texas State University 2004-04-01
• Series: Electronic Journal of Differential Equations
• Subjects: Fixed-point theorems; time scales; dynamic equations; cone.
• Online Access: http://ejde.math.txstate.edu/Volumes/2004/47/abstr.html

We establish the existence of multiple positive solutions to the nonlinear second-order triple-point boundary-value problem on time scales, $$displaylines{ u^{Delta abla}(t)+h(t)f(t,u(t))=0, cr u(a)=alpha u(b)+delta u^Delta(a),quad eta u(c)+gamma u^Delta(c)=0 }$$ for $tin[a,c]subsetmathbb{T}$, where $mathbb{T}$ is a time scale, $eta, gamma, deltage 0$ with $Beta+gamma>0$, $0<alpha<frac{c-a}{c-b}$ and $bin(a,c)subsetmathbb{T}$.