摘要
In this paper the existence and nonexistence of non-trivial solution for the Cauchy problem of the form{ut=div（｜Δ↓u｜^p-2Δ↓u）-偏d/偏dxibi（u）-uq u（x,0）=0 （x,t）∈ST=R^N×（0,T）,x∈R^N／{0}are studied. We assume that ｜bi′（s）｜≤ Ms^m-1, and proved that if p〉2,0〈q〈p-1＋p/N,0≤m〈p-1＋p/N,then the problem has a solution;if P〉2,q〉P-1＋p/N,0≤m≤q（p＋Np-N-1）/p＋nP-N,then the problem has no solution;if p〉2,p-1〈q〈p-1＋p/N,0≤m〈q,then the problem has a very singular solution;if p〉2,q〉p-1＋p/N,0〈m〈q-p/2N,then the problem has no very singular solution.we use P.D.E.methods such as regularization, Moser iteration and Imbedding Theorem.
