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Existence of multiple positive solutions of inhomogeneous semilinear elliptic problems in unbounded domains

Published online by Cambridge University Press:  14 November 2011

Xi-Ping Zhu  and
Huan-Song Zhou
Xi-Ping Zhu
Affiliation:
Department of Mathematics, Zhongshan University, Guangzhou 510275, PR China
Huan-Song Zhou
Affiliation:
Wuhan Institute of Mathematical Sciences, Academia Sinica, PO Box 71007, Wuhan 430071, PR China
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Synopsis

By using the concentration-compactness method of Lions [14, 16] and the mountain pass theorem of Ambrosetti and Rabinowitz [3], through a careful inspection of the energy balance for some sequence of approximated solutions, we show that under suitable conditions on f and h, the inhomogeneous problem. −Δu + c2u = λ(f(u) + h(x)) for x ∈ Ω (Ω is an exterior domain in ℝN, N≧ 3) and has at least two positive solutions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 115 , Issue 3-4 , 1990 , pp. 301 - 318
Copyright
Copyright © Royal Society of Edinburgh 1990

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