在這篇論文中，我們考慮由電漿物理所衍生之Grad-Shafranov 方程式(請參考郝玲妮教授與其博士生傅瑋宗之文章[2]、[3])。利用正規擾動方法，我們觀察此方程(在一維情況下)之正解，對其參數Kappa 之極限行為。此外，我們亦提供一些徑向解的結構，諸如全域存在性、唯一性以及漸進行為。 In this thesis, we consider a new type of Grad-Shafranov equation : $$displaystyle Delta u=Big(1+frac{cu}{kappa}Big)^{-kappa+frac{1}{2}} $$ arising from the plasma physics (see Ref. cite{HF1} and cite{HF2} by L.-N. Hau and W.-Z. Fu). Using the method of regular perturbation, we investigate the limiting behavior of positive solutions (for 1D case) with respect to the parameter Kappa $kappa$ (as $kappa o infty$). In addition, the global existence, uniqueness and asymptotic behavior of positive radial solutions will be proved as well.
