The original Strum-Liouville type of equation is tuned suitably to study the pulsational properties of gaseous spheres of non-uniform densities from centre to surface, which are non-rotating, have solid body rotation or are differentially rotating as well as those which are varying by tidal effects. The eign-frequencies of radial oscillations have been computed numerically for certain polytropic stellar models of non-uniform densities. In order to analyse the effect of non-radial modes of oscillations, the linearised system of differential equations that govern non-radial modes of oscillations, have also been developed and solved for certain polytropic models. It has been observed that with the exception of purely radial oscillations, which are unstable only when $\gamma <4/3$ ($\gamma$ is the ratio of molar specific heats), there also exist non-radial modes of oscillations. It is necessary to consider radial as well as non-radial nodes of oscillations in order to ascertain the stabilities of the existence of any assumed model.

对原始的Strum-Liouville型方程进行了适当的调整，以研究从中心到表面的密度不均匀的气态球的脉动特性，这些气态球是不旋转的，具有固体旋转或微分旋转的以及变化的受潮汐影响。对于某些密度不均匀的多星恒星模型，已经通过数值计算了径向振荡的固有频率。为了分析振荡的非径向模式的影响，还开发了用于控制振荡的非径向模式的微分方程线性化系统，并对其进行了求解。已经观察到，除了纯径向振动之外，仅在径向振动时才是不稳定的。$\gamma <4/3$ （$\gamma$是摩尔比热的比率），也存在非径向振荡模式。为了确定任何假定模型存在的稳定性，有必要考虑振动的径向和非径向节点。