【摘要】 证明了当λ<λ₁且足够靠近λ₁时方程■存在正解（其中λ₁是算子■的第一个特征值）;讨论了更一般的方程,给出了方程存在正解的充分条件.解决了H.Brezis 和L.Nirenberg 在文[1]中提出的一个问题,并把（1）中对应的结果作为特例重新得到.更多还原

【Abstract】 We study the existence of positive solution of variable coefficient equation.We have proved that the equation-（?）=u^p+λu（p=（n+2）/（n-2）,n≥3）exists a positive solution when λ<λ₁ and near λ₁[λ₁ is the first eigenvalue of theoperator Lu=-（?）.Some existence results of the equation（?）=u^p+h（x）u are obtained.A problem of [1] is solved and theresults of [1] is deduced as a special case of ours.This work is supported in part by the Foundation of Zhongshan UniversityAdvanced Research Centre.更多还原