Multiplicity of positive solutions for a nonlinear \(m\)-point BVP with sign changing nonlinearity on time scales (Q711515)

By using fixed point theorems in cones, the authors obtain a sufficient condition for the existence of a positive solution for the nonlinear \(m\)-point boundary value problem \[ \begin{aligned} &(\phi(u^{\triangle}))^{\nabla}+a(t)f(t,u(t))=0,\quad t\in(0,T),\\ &u(0)=\sum^{m-2}_{i=1}a_i u(\xi_i),\quad \phi(u^{\triangle}(T))=\sum^{m-2}_{i=1}b_i\phi(u^{\triangle}(\xi_i)),\end{aligned} \] where \(\phi:\mathbb R\to\mathbb R\) is an increasing homeomorphism and positive homomorphism with \(\phi(0)=0\). The nonlinear term \(f\) may change sign.