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Existence of multiple positive solutions for −Δu−μ(u/∣x∣2)=u2*−1+σf(x)

✍ Scribed by Ting Cheng; Charles Xuejin Zhao

Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
250 KB
Volume
25
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

In this paper, we consider the semilinear elliptic problem

where Ω⊂ℝ^N^ (N⩾3) is a bounded smooth domain such that 0∈Ω, σ>0 is a real parameter, $$\mu < \overline{\mu } = (N - 2)^{2} /4$$ and f(x) is some given function in L^∞^(Ω) such that f(x)⩾0, f(x)≢0 in Ω. Some existence results of multiple solutions have been obtained by implicit function theorem, monotone iteration method and Mountain Pass Lemma. Copyright © 2002 John Wiley & Sons, Ltd.

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