a1 Young Scientist Lab. of Mathematical Physics, Wuhan Institute of Mathematical Sciences, Academia Sinica, P.O. Box 71007, Wuhan 430071, People's Republic of China
We consider the following problem
where for all ≦f(x,u)≦c1up-1 + c2u for all x ∈ℝN,u≧0 with c1>0,c2∈(0, 1), 2<p<(2N/(N – 2)) if N ≧ 3, 2 ≧ + ∝ if N = 2. We prove that (*) has at least two positive solutions if
and h≩0 in ℝN, where S is the best Sobolev constant and
(Received September 26 1994)
(Revised January 17 1995)
* Supported by National Natural Science Foundation of China and C.G. project of the Science and Technology Committee of Wuhan.