Oscillation theorems for self-adjoint matrix Hamiltonian systems involving general means

Abstract

By use of monotone functionals and positive linear functionals, a generalized Riccati transformation and the general means technique, some new oscillation criteria for the following self-adjoint Hamiltonian matrix system

(E)$$\text{X′(t)=A(t)X(t)+B(t)Y(t),}\text{Y′(t)=C(t)X(t)−A}{}^{\mathrm{\ast }}\text{(t)Y(t)}$$

are obtained. The results obtained improve and complement that of Kumari et al. (2000) on Kamenev type theorems. Moreover, these results generalize and improve earlier results due to Meng (2002) for (E), Erbe et al. (1993), Meng et al. (1998) and Wang (2001) for (P(t)X′(t))′+Q(t)X(t)=0 or its special cases, and Wong (2001) for the scalar system x″(t)+q(t)x(t)=0.