Multiple solutions for semilinear elliptic equations with nonlinear boundary conditions

Junichi Harada, Mitsuharu Otani

    Research output: Contribution to journalArticle

    Abstract

    We consider the elliptic problem with nonlinear boundary conditions: Δu + bu = f (x, u) in Ω, - ∂ νu = {Pipe}u{Pipe} q-1u - g(u) on dΩ, where Ω is a bounded domain in ℝ n. Proving the existence of solutions of this problem relies essentially on a variational argument. However, since L q+1(∂Ω) ⊂ H 1(Ω) does not hold for large q, the standard variational method can not be applied directly. To overcome this difficulty, we use approximation methods and uniform a priori estimates for solutions of approximate equations.

    Original languageEnglish
    Pages (from-to)1-9
    Number of pages9
    JournalElectronic Journal of Differential Equations
    Volume2012
    Publication statusPublished - 2012 Feb 23

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    Uniform Estimates
    Semilinear Elliptic Equations
    Nonlinear Boundary Conditions
    Multiple Solutions
    A Priori Estimates
    Variational Methods
    Approximation Methods
    Elliptic Problems
    Existence of Solutions
    Bounded Domain
    Standards

    Keywords

    • Nonlinear boundary conditions

    ASJC Scopus subject areas

    • Analysis

    Cite this

    Multiple solutions for semilinear elliptic equations with nonlinear boundary conditions. / Harada, Junichi; Otani, Mitsuharu.

    In: Electronic Journal of Differential Equations, Vol. 2012, 23.02.2012, p. 1-9.

    Research output: Contribution to journalArticle

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