Lyapunov-type inequalities for the first-order nonlinear Hamiltonian systems

In this paper, we establish several new Lyapunov-type inequalities for the first-order nonlinear Hamiltonian system {x′(t)=α(t)x(t)+β(t)|y(t)|μ−2y(t),y′(t)=−γ(t)|x(t)|ν−2x(t)−α(t)y(t), which generalize or improve all related existing ones.