Fourth order elliptic boundary value problem with nonlinear term decaying at the origin

摘要

We consider the number of the weak solutions for some fourth order elliptic boundary value problem with bounded nonlinear term decaying at the origin. We get a theorem, which shows the existence of the bounded solution for this problem. We obtain this result by approaching the variational method and using the generalized mountain pass theorem for the fourth order elliptic problem with bounded nonlinear term. MSC:35J30, 35J40.