Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Multiple positive solutions of nonhomogeneous semilinear elliptic equations in N*

Cao Dao-Mina1 and Zhou Huan-Songa1

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.