关键词: 正解, 存在性, 不存在性

Abstract: Positive solutions of quasilinear elliptic equations with degeneracy and singularity for a class of p-Laplace problems are discussed. For one dimension, the conditions of boundless solutions are given. And for multi-dimension the conditions of the problems with sufficiently regular and star-shaped domain are also given, which have no solutions in Sobolev space. The techniques including functional transformation were used to overcome the difficulties coming from the degeneracy and singularity of the problems. A further complementarity of the equations for p≠2 is given, too.

Key words: positive solution, existence, nonexistence