奇异哈密顿微分系统的粘结引理和亏指数

Patching Lemma and Deficiency Indices for Singular Hamiltonian Differential Systems

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摘要建立了奇异哈密顿微分系统的"粘结"引理,这是H.D.Niessen和A.Zettl关于二阶微分方程相应结果的推广.同时也得到了Rellich和Rosenberger关于二阶微分方程非振动结果在奇异哈密顿微分系统上的推广形式,并由此建立了奇异哈密顿微分系统极限点型判断准则.该结果不但推广了綦、陈的相应结果,包含了S.L.Clark和F.Gesztesy的结果,同时也得到了奇异哈密顿微分系统的Hartman型极限点型判断准则. The ＂patching＂ lemma for singular Hamiltonian differential systems is obtained, which is the extension version of the corresponding result of H.D. Niessen and A. Zettl for second order differential equations. With applications, the non-oscillation criterion of Rellich and Rosenberger type is generalized to singular Hamiltonian differential systems and the limit- point criteria of J. Qi and Sh. Chen, S.L. Clark and F. Gesztesy are improved.

作者杨杰綦建刚景海斌

机构地区山东师范大学数学科学学院山东大学威海分校数学与统计学院河北建筑工程学院数理系

出处《数学物理学报（A辑）》 CSCD 北大核心 2011年第3期652-661,共10页 Acta Mathematica Scientia

基金山东省自然科学基金(Y2008A02)资助

关键词哈密顿微分系统振动性亏指数极限点型 Hamiltonian differential system Oscillation Deficiency index Limit-point case.

分类号 O175 [理学—基础数学]

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数学物理学报（A辑）

2011年第3期

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奇异哈密顿微分系统的粘结引理和亏指数

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