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Existence of multiple positive solutions for −Δ u −μ( u /∣ x ∣ 2 )= u 2*−1 +σ f ( x )
Author(s) -
Cheng Ting,
Zhao Charles Xuejin
Publication year - 2002
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.339
Subject(s) - mathematics , monotone polygon , bounded function , domain (mathematical analysis) , lemma (botany) , combinatorics , function (biology) , monotonic function , mathematical analysis , geometry , ecology , poaceae , evolutionary biology , biology
In this paper, we consider the semilinear elliptic problem$$- \Delta u - \mu (u/\left| x \right|^{2} ) = u^{{2* - 1}} + \sigma f(x)\,u > 0,\,u \in H_{0}^{1} (\Omega )$$ 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.