两个一阶线性常微分方程组解的性态
The behavior of solutions of the systems of two first order linear ordinary differential equations
摘要：
本文用Riccati方程方法研究两个一阶线性常微分方程组解的性态。揭示了这些系统的各种振荡形式和规律性。得到了Leighton定理的一个推广。导出了二阶线性微分方程的三个新原理。证明了上述系统的稳定性和非共轭性准则，并对后一类系统的解给出了估计。
英文摘要：
The Riccati equation method is used for study the behavior of solutions of the systems of two linear first order ordinary differential equations. All types of oscillation and regularity of these system are revealed. A generalization of Leighton's theorem is obtained. Three new principles for the second order linear differential equations are derived. Stability and non conjugation criteria are proved for the mentioned systems, as well as estimates are obtained for the solutions of the last ones.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
