Multiple Solutions For P-biharmonic Equations With Hardy Potential

In this paper, firstly we study the p-biharmonic equation with Hardy potential in RN where D is the completion of C∞/0(RN) under the norm and a(x) satisfies the ollowing condition: (A) α(x)> 0 and α(x) ∈ Lq(RN), where1/q+r/p*= 1. By using the method of invariant sets of decending flow, we obtain the existence of a positive solution, a negative solution and a sequence of sign-changing solutions; Sec-ondly, we consider the p-biharmonic equation with Hardy potential under oblique boundary value condition where Ω (?) RN is a bounded smooth domain,0 ∈ Ω,0< μ<μN,P and △2/pu = △(|△u|p-2A△u) is p-biharmonic operator, a> 0 is a parameter. If f(x,t) is superlinear at t = 0 and subcritical growth. Similarly, by using the method of invariant sets of decending flow, we also obtain the existence of a positive solution, a negative solution and a sign-changing solution. Moreover, if f(x,t) is odd in t, we obtain a sequence of sign-cnangmg solutions.