全空间上一类半线性双调和方程正解的衰减

Decay Rate of Solutions to An Inhomogenerous Semilinear Biharmonic Equation in Entire Space

研究如下非齐次双调和方程-△~2u+u^p+f(x)=0,x∈R^n(*)正解的存在性,其中△~2是双调和算子,p>1,n≥5,f≠0.在文献[16[的基础上,得到:对f给定条件,方程(*)有一类不同于文献[16]的两种衰减的正解.

In this paper, we consider the existence of the positive solutions for the inhomogeneous biharmonic equation -△^2u＋u^p＋f（x）=0,x∈R^n（＊） where △^2 is the biharmonic operator, p 〉 1, n ≥ 5 Based on [16], the existence of solutions with the under the assumptions on f. and f 0 is a given nonnegative function. third decay rate at infinity are established under the assumptions on f.