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

Satoshi Hashimoto, Mitsuharu Otani

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    2 Citations (Scopus)


    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.

    Original languageEnglish
    Pages (from-to)323-333
    Number of pages11
    JournalDiscrete and Continuous Dynamical Systems
    Issue number2
    Publication statusPublished - 2007 Oct



    • Exterior domain
    • P-Laplacian
    • Supercritical exponent

    ASJC Scopus subject areas

    • Mathematics(all)
    • Discrete Mathematics and Combinatorics
    • Applied Mathematics
    • Analysis

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