In this paper, we investigate new Lyapunov-type inequalities for Hamiltonian-type problem w′ = η (x) w + ∣∣∣y∣∣∣p−2 y( 1 + ∣∣∣y∣∣∣p ) p−1p y′ = −σ (x) |w| β−2 w( 1 + |w|β ) β−1 β − η (x) y involving the p-prescribed curvature operator Φp (v) = |v|p−2 v( 1 + |v|p ) p−1 p , p > 1, under Dirichlet boundary condition.