Positive Solutions for System of First-Order Dynamic Equations

Abstract

We study the existence of positive solutions to the system of nonlinear first-order periodic boundary value problems on time scales xΔ(t)+P(t)x(σ(t))=F(t,x(σ(t))), t∈[0,T]T, x(0)=x(σ(T)), by using a well-known fixed point theorem in cones. Moreover, we characterize the eigenvalue intervals for xΔ(t)+P(t)x(σ(t))=λH(t)G(x(σ(t))), t∈[0,T]T, x(0)=x(σ(T)).