Existence of nontrivial solutions for some elliptic equations with supercritical nonlinearity in exterior domains

Satoshi Hashimoto*, Mitsuharu Otani

*この研究の対応する著者

    研究成果: Article査読

    2 被引用数 (Scopus)

    抄録

    The existence of positive solutions is discussed for some nonlinear elliptic equations involving the nonlinear terms with the growth order of super-critical exponents in exterior domains of balls such as -Δu = u β in Ω, ((N + 2)/(N - 2) < β), u = 0 on ∂B, with Ω = ℝN\Ω̄ where Ω0 is the open ball. To recover the compactness of the embedding L β+1(Ω) ⊂ H0 1(Ω, we work in the class of radially symmetric functions and introduce a new transformation, which reduces our problems to some nonlinear elliptic equations in annuli but with coefficients which have some singularity on the boundary. The difficulty caused by the singularity on the boundary will be managed by the arguments developed in our previous work.

    本文言語English
    ページ(範囲)323-333
    ページ数11
    ジャーナルDiscrete and Continuous Dynamical Systems
    19
    2
    出版ステータスPublished - 2007 10月

    ASJC Scopus subject areas

    • 数学 (全般)
    • 離散数学と組合せ数学
    • 応用数学
    • 分析

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