Oscillation Criteria for Linear Matrix Hamiltonian Systems

Abstract

AbstractIn this paper we present oscillation criteria in terms of the coefficient functions for the matrix linear Hamiltonian system U′=A(x)U+B(x)V, V′=C(x)U−A*(x)V under the hypothesis H:A(x), B(x)=B*(x)>0 and C(x)=C*(x) are n×n matrices of real valued continuous functions on the interval I=[a, ∞), (−∞<a). These criteria generalize earlier results due to Etgen and Pawlowski (1976), Erbe, Qingkai Kong and Shigui Ruan (1993), and Fanwei Meng, Jizhong Wang, and Zhaowen Zheng (1998) for the system (P(x)U′)′+Q(x)U=0 or its special cases