Entire positive solutions for an inhomogeneous semilinear biharmonic equation

摘要

In this paper, we investigate the entire positive Solutions for the inhomogeneous biharmonic equation - Delta(2)u + u(p) + f(x) = 0 in R-n, (*) where Delta(2) is the biharmonic operator, p > 1, n >= 5 and 0 not equivalent to f is an element of C(R-n) is a given nonnegative function, Based on the results on the biharmonic equation in [Q.Y. Dai, Entire positive solutions for inhomogeneous semilinear elliptic systems, Glasgow Math. J 47 (2005) 97-114], we obtain the optimal "decay coefficient" of the inhomogeneous term f for existence and nonexistence. And also, we obtain that there exist at least two types of decay solutions at infinity with the assumptions on f. (C) 2008 Elsevier Ltd. All rights reserved.