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

S0308210500022836_eqn1

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

S0308210500022836_eqnU2

and h≩0 in ℝN, where S is the best Sobolev constant and

S0308210500022836_eqnU3

(Received September 26 1994)

(Revised January 17 1995)

Footnotes

* Supported by National Natural Science Foundation of China and C.G. project of the Science and Technology Committee of Wuhan.