Application On Doubling Lemma And Monotonicity Formula For Elliptic Equations

This academic dissertation is concerned about the application of doubling lemma and monotonicity formula for elliptic equations.There are many nonexistence results of positive solution of quasilinear el-liptic systems with m-Laplacians.According to the Liouville theorems of those systems on Rn,we obtain the singularity estimates of the positive C1-weak so-lutions on bounded or unbounded domain(but it is not Rn)and their decay rates on the exterior domain when |x|?oo.The doubling lemma which is developed by Polacik-Quittner-Souplet plays a key role here.In addition,the corresponding results of several special examples are presented.Next,we consider the nonexistence of positive stable solutions of a weight-ed Lane-Emden equation.First we obtain a monotonicity formula by choosing a proper energy.Based on this result,we prove that the nonnegative homogeneous stable solution must be a trivial solution.Finally,we prove the nonexistence of positive stable solutions when p? P+(n,?),where P+(n,?)is the Joseph-Lundgren exponent.