| 1 | Positive solutions of p-th Yamabe type equations on graphs显示文摘Let G=(V,E)be a finite connected weighted graph,and assume 1≤α≤p≤q.In this paper,we consider the p-th Yamabe type equation -△pu +hu^q-1=λfu^α-1 on G,where △p is the p-th discrete graph Laplacian, h <0 and f >0 are real functions defined on all vertices of G.Instead of H.Ge's approach [Proc.Amer.Math.Soc.,2018,146(5):2219-2224],we adopt a new approach,and prove that the above equation always has a positive solution u >0 for some constant λ∈R.In particular,when q=p,our result generalizes Ge's main theorem from the case of α≥P>1 to the case of 1≤α≤p.It is interesting that our new approach can also work in the case of α≥p>1. | Xiaoxiao ZHANG Aijin LIN | 2018 | Frontiers of Mathematics in China2018，13，6： | 0 |
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