Triple positive solutions for third-order \(m\)-point boundary value problems on time scales (Q1040090)

Summary: We study the following third-order \(m\)-point boundary value problems on time scales \[ (\varphi(u\Delta\nabla))^\nabla+a(t)f(u(t))=0,\quad t\in [0,T]_{\mathbf T}, \] \[ u(0)=\sum^{m-2}_{i=1}b_iu(\xi_i),\quad u\Delta(T)=0,\quad \varphi(u^{\Delta\nabla}(0))=\sum^{m-2}{i=1}c_i\varphi(u\Delta \nabla(\xi_i)), \] where \(\varphi:R\to R\) is an increasing homeomorphism, \(\varphi(0)=0\), \(0<\xi_1<\cdots<\xi_{m-2}<\rho(T)\). We obtain the existence of three positive solutions by using a fixed-point theorem in cones.