Positive solutions for system of first-order dynamic equations (Q980797)

Summary: We study the existence of positive solutions to the system of nonlinear first-order periodic boundary value problems on time scales \[ x^\Delta(t)+P(t)x(\sigma(t))=F(t,x(\sigma(t))),\quad t\in [0,T]_{\mathbb T},\;x(0)=x(\sigma(T)), \] by using a well-known fixed point theorem in cones. Moreover, we characterize the eigenvalue intervals for \[ x^\Delta(t)+P(t)x(\sigma(t))=\lambda H(t)G(x(\sigma(t))),\quad t\in [0,T]_{\mathbb T},\quad x(0)=x(\sigma(T)). \]