Nontrivial Solutions To The P-harmonic Equation With Nonlinearity Asymptotic To |t|^p-2t At Infinity

We consider the following p-harmonic problem (?) where m>0 is a constant,N>2p? 4 and(?)uniformly in x,which implies that f(x,t)does not satisfy the Ambrosetti-Rabinowitz type condition.By showing the Pohozaev identity for weak solutions to the limited problem of the above p-harmonic equation and using a variant version of Mountain Pass Theo-rem,we prove the existence and nonexistence of nontrivial solutions to the above equation.Moreover,if f(x,u)? f(u),the existence of a ground state solution and the nonexistence of nontrivial solutions to the above problem is also proved by using artificial constraint method and the Pohozaev identity.