复系数奇异Sturm-Liouville方程的极限点和极限圆分类

Limit-point and Limit-circle Classification of Singular Sturm-Liouville Equations with Complex Coefficients

该文利用对称Hamilton微分系统的极限点、极限圆分类理论(不同于B.M.Brown等人采用的方法),给出了复系数奇异Sturm-Liouville方程的Sims分类:极限点1型、极限点2型和极限圆型;并且建立了极限点1型的两个判别准则;最后通过举例肯定地回答了B.M.Brown等人提出的开问题.

By using limit-point（circle） classification theory of symmetric Hamiltonian differential systems,different from the method used by B.M.Brown et al,the paper gives the Sims classification of singular Sturm-Liouville equations with complex coefficients：limit-point-1 case, limit-point-2 case and limit-circle case.Then two limit-point-1 case criteria are obtained.Furthermore, the authors give an affirmative answer to the open problem of B.M.Brown et al by an example.