Spectrum of a class of fourth order left-definite differential operators期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Spectrum of a class of fourth order left-definite differential operators

Authors:

Affiliation:

[1]Dept. of Math., Inner Mongolia Univ. of Tech., Hohhot 010051, China. [2]Dept. of Math., Inner Mongolia Univ., Hohhot 010021, China.

Abstract:

The spectrum of a class of fourth order left-definite differential operators is studied. By using the theory of indefinite differential operators in Krein space and the relationship between left-definite and right-definite operators, the following conclusions are obtained: if a fourth order differential operator with a self-adjoint boundary condition that is left-definite and right-indefinite, then all its eigenvalues are real, and there exist countably infinitely many positive and negative eigenvalues which are unbounded from below and above, have no finite cluster point and can be indexed to satisfy the inequality

$cdots leqslant lambda _{ - 2} leqslant lambda _{ - 1} leqslant lambda _{ - 0} < 0 < lambda _0 leqslant lambda _1 leqslant lambda _2 leqslant cdots .$

Supported by the National Natural Science Foundation of China(10561005), the Doctor’s Discipline Fund of the Ministry of Education of China(20040126008).

Keywords:

left-definite differential operator right-definite differential operator Krein space spectrum eigenvalue

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