Existence And Multiplicity Of Solutions For Linear Elliptic Equations (group) Proposed Two Types Of Solution

In this paper,we investigate the existence and multiplicity of positive solutions for some quasilinear elliptic problems.In chapter1, using variational methods, we establish the existence of positive solutions for a class of quasilinear elliptic problem where△pu=div(|(?)u|p-2(?)u) with1<p<N,f:R→R is continuous having a subcritical growth and V is a nonnegative potential, which satisfies lim|x|→+∞V(x)=0.In chapter2, we investigate how the coefficient f(x) affects the number of posi-tive solutions of the following quasilinear elliptic systems where O∈Ω(?) RN is a bounded domain, a>1,β>1and1<p<q<a+β=p*=Np/N-p for N＞2p.