Asymptotic Behavior Of Nonminimal Solutions Of Nonlinear Elliptic Equation -div(a(x)(?)u)=?b(x)e~u

In this thesis,we study the Emden-Fowler equation on the bounded smooth domain? in R2#12 where ?>0,A(x)=(aij(x))is a second-order positive definite symmetric matrix.aij(x)(i,j=1,2),b(x)are smooth functions on ?,and satisfy the condition(H):0<??aij(x),b(x)??<?,i,j=1,2.We consider the asymptotic behavior of nonminimal solutions u? as ??0,we prove that u? will be blow-up at some critical points of a(x)=(?),meanwhile,we prove that,we have u? convergent to u*weakly in W1,p(?)for any p?(1,2)as ??0,u*satisfies#12 where mi?N*,S????,S={?ixi?,?={x??;?a(x)=0}.