一类具幂对数乘积系数的微分算子的离散谱  

On the Discreteness Spectrum of a Class of Differential Operators with product of Power Function and Logarithmic Function

作　　者：邱洁[1] 王万义[1] 彭艳伟 

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022

出　　处：《阴山学刊（自然科学版）》2013年第4期5-10,共6页Yinshan Academic Journal(Natural Science Edition)

基　　金：国家自然科学基金项目(10961019)

摘　　要：通过利用Sobolev嵌入的紧性、算子的直和分解原理、二次型比较的方法及微分方程解的振荡原则等方法研究了一类系数中含有对数函数与幂函数乘积的2n阶实系数对称微分算子,得到此类微分算子的谱是离散的充分必要条件.A class of 2n- th order symmetric differential operators with real valued coefficients which contain product of power function and logarithmic function. A sufficient and necessary condition is given which ensures that the spectrum of differential operators is discrete by means of the compactness of Sobolev spaces, the method of de- composition into direct sum of operator , comparison of quadratic form and oscillation theory of differential equa- tlons

关 键 词：微分算子 离散谱 本质谱 

分 类 号：O175.3[理学—数学]