Liouville Type Result And Regularity Of Solutions Of A Weighted Elliptic Equation

TThis paper studies structure of nonnegative entire solutions of a weighted elliptic equation. A Liouville type result is established for nonnegative solutions of the equation.Meanwhile, some existence and regularity results are also obtained. Moreover, the main results in this paper imply that the number ps is the critical value of the Dirichlet problems of the related equation.WWe intend to separate the dissertation into four chapters as follows:In Chapter one. we first present the applications practical and related work of the weighted elliptic equation. Then, the main work of this paper is briefly introduced. At last,we recall the knowledge of elliptic equation and nonlinear analysis involved in this paper.In Chapter two, firstly, we prove the existence of nontrivial nonnegative solutions of the equation and improve their regularity results. In a word, we obtain some removable singularity results for solutions to the (P) under different conditions.In Chalpter three,we obtain the strict monotonicity of |x|(N'-2)/2u(x). Then we obtain the Liouville type result for nonnegative entire solntions of the equation.In Chapter four,two obtain the non-existence of positive C2(?\{0})?C(?) -solution.and thus prove these results .Iu the end,we give some remarks on the positive singular solutions of(P).