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Multiple positive solutions of nonhomogeneous semilinear elliptic equations in ℝN*

Published online by Cambridge University Press:  14 November 2011

Cao Dao-Min  and
Zhou Huan-Song
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
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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
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 2 , 1996 , pp. 443 - 463
Copyright
Copyright © Royal Society of Edinburgh 1996

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