一类双调和方程基态解的存在性

The existence of ground-state solutions to a class of biharmonic elliptic equations

研究以下双调和非线性椭圆方程:{Δ2 u+V(x)u=f(x,u)于RN,u∈H2(RN).其中V(x)是具有正下界的连续周期函数,非线性项f(x,u)∈C1,F(x,u)∶=∫u0f(x,s)ds具有超线性增长(但不一定满足AR条件),主要用极小化方法证明上述方程的基态解的存在性.该结果是文献[3]中半线性椭圆方程的结果在双调和型方程中的推广.

We considered the following equation△^2u＋V（x）u=f（x,u）于R^N,u∈H^2（R^N）.where V was a positive continuous periodic function, the nonlinearityf（x,u）∈C^1,F（x,u）：= f（x,s）dssatisfied super-quadratic condition but without （AR） condition. We proved the existence of ground-state solution for the above equation. Our result generalized a similar result in reference[3] to biharmonic type problem.