Proceedings of the Royal Society of Edinburgh: Section A Mathematics

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Research Article

Interval oscillation criteria for self-adjoint matrix Hamiltonian systems


Qigui Yanga1 and Yun Tanga2



a1 Department of Mathematics, South China University of Technology, Guangzhou 510640, People's Republic of China (yangqigui@263.net)

a2 Department of Mathematics, Tsinghua University, Beijing 100084, People's Republic of China (ytang@math.tsinghua.edu.cn)

Article author query

Yang Q [Google Scholar]
Tang Y [Google Scholar]

Abstract

By using a monotonic functional on a suitable matrix space, some new oscillation criteria for self-adjoint matrix Hamiltonian systems are obtained. They are different from most known results in the sense that the results of this paper are based on information only for a sequence of subintervals of [t0, ∞), rather than for the whole half-line. We develop new criteria for oscillations involving monotonic functionals instead of positive linear functionals or the largest eigenvalue. The results are new, even for the particular case of self-adjoint second-differential systems which can be applied to extreme cases such asS0308210500004285inline001

(Received April 13 2004)

(Accepted March 09 2005)