摘要
利用左定微分算子与相应的右定微分算子之间的关系来研究左定微分算子.首先给出四阶奇异微分算子的自共轭域;接着利用主解与Friedrichs扩张寻找最小算子的正的自共轭扩张;最后通过系数、区间端点和边界条件给出四阶奇异微分算子左定性的充要条件以及相应的左定边值矩阵的情形.
In this paper, a class of fourth-order singular differential operators is studied. The relationship between left-definite differential operators and the corresponding right-definite ones is used. Firstly, the self-adjoint domains of fourth-order singular differential operators are given. Secondly, positive self-adjoint extension of the minimal operator is obtained, in which the principal solution and Friedrichs expansion of the operators are used. Finally, the necessary and sufficient conditions of the operator＇s left-definiteness are got, which depend on the coefficients, the endpoints and the boundary conditions. Moreover, all the cases of the left-definite boundary matrix are given here.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
2012年第2期182-192,共11页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
国家自然科学基金(11171295)
关键词
四阶奇异微分算子
左定边界条件
边值矩阵
fourth-order singular differential operators
left-definite boundary conditions
bound- ary matrix
