一类带有奇异项的拟线性问题正解的存在性

通过扰动方法,Schauder不动点定理以及变量替换方法研究了一类带有奇异项的拟线性方程正解的存在性.首先利用变量替换将拟线性问题转化为半线性问题,再通过Schauder不动点定理得到扰动问题的正古典解,最后通过对扰动问题的解序列取极限得到原始问题的解,并利用反证法得到正解的唯一性.

Existence of positive solutions for quasilinear problems with a singularity

The existence of positive solutions for a class of quasilinear equations with a singularity is studied by the perturbation method,the Schauder fixed point theorem and the variable substitution method. First,the quasilinear problem is transformed into a semi-linear problem by a variable substitution,and then the positive classical solution of the perturbation problem is obtained by the Schauder fixed point theorem. Finally,the solution of the original problem is obtained by taking the limit of the solution sequence of the perturbation problem,and the uniqueness of positive solution is obtained by using the method of absurdity.