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Multiple positive solutions of nonhomogeneous semilinear elliptic equations in N*

Published online by Cambridge University Press:  14 November 2011

Cao Dao-Min
Affiliation:
Young Scientist Lab. of Mathematical Physics, Wuhan Institute of Mathematical Sciences, Academia Sinica, P.O. Box 71007, Wuhan 430071, People's Republic of China
Zhou Huan-Song
Affiliation:
Young Scientist Lab. of Mathematical Physics, Wuhan Institute of Mathematical Sciences, Academia Sinica, P.O. Box 71007, Wuhan 430071, People's Republic of China

Extract

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

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1996

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