Oscillation criteria related to integral averaging technique for linear matrix Hamiltonian systems
New oscillation criteria are established for the linear matrix Hamiltonian system \[ U'=A(x)U+B(x)V,\quad V'=C(x)U-A^*(x)V, \tag{*} \] where \(A(x)\), \(B(x)=B^*(x)>0\) and \(C(x)=C^*(x)\) are \(n\times n\)-matrices of real-valued continuous functions on the interval \(I=[x_0,\infty)\). These results are obtained by using the generalized Riccati technique and the integral averaging technique introduced by \textit{Ch. G. Philos} (1989), and they generalize a number of existing results, e.g., results of \textit{L. H. Erbe, Q. Kong} and \textit{S. Ruan} [Proc. Am. Math. Soc. 117, No. 4, 957--962 (1993; Zbl 0777.34024)], \textit{I. Sowjanya Kumari} and \textit{S. Umamaheswaram} [J. Differ. Equations 165, No. 1, 174--198 (2000; Zbl 0970.34025)], \textit{H. J. Li} [J. Math. Anal. Appl. 194, 217--234 (1995; Zbl 0836.34033)] and \textit{Z. Zheng, F. Meng} and \textit{Y. Yu} [Acta Math. Sin. 41, No. 6, 1231--1238 (1998; Zbl 1018.34033)]. Three examples illustrate various oscillation criteria.
scientific article; zbMATH DE number 2093791