Second-order periodic boundary value problems on time scales (Q1767973)

The author considers the existence of solutions of periodic boundary value problem for second-order nonlinear dynamic equations on time scales \[ -y^{\Delta\nabla}(t)+q(t)y(t)=f(t,y(t)),\quad t\in [a,b], \] \[ y(\rho(a))=y(b),\quad y^\Delta(\rho(a))=y^\Delta(b), \] where \([a,b]\) is a subset of the time sale \(T\); \(h^\Delta(t)\) is the delta derivative of \(h\), \(h^\nabla(t)\) is the nabla derivative of \(h\).