一类可缩区域上半线性椭圆型方程多个正解的存在性

MUTIPLICITY OF POSITIVE SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATIONS WITH CRITICAL SOBOLEV EXPONENT IN SOME CONTRACTIBLE DOMAINS

本文考虑下列方程其中，为一类有界可缩区域，充分光滑，λ∈Ｒ，ｖ为的单位外法向量，ｐ＝为临界指标．我们证明了λ＞０充分大时，上述方程具有多个正解．

In this papar, we consider the following problem where is a bounded. and contractible domain with smooth boundary, λ>0 is a constant, and v is the unit normal vector of , is the critical exponent. We prove the existence of mutiple positive solutions for sufficiently large λ.