Elliptic equations with competing rapidly varying nonlinearities and boundary blow-up

Florica Corina Cîrstea*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    32 Citations (Scopus)

    Abstract

    We prove that δu + au = b(x)f(u) possesses a unique positive solution such that limdist(x,∂ω)→0 u(x) = ∞, where ω is a smooth bounded domain in ℝN and a ∈ ℝ. Here b is a smooth function on ω which is positive in ω and may vanish on ∂ω (possibly at a very degenerate rate such as exp(-[dist(x, ∂ω)]q) with q lt; 0). We assume that f is locally Lipschitz continuous on [0,∞) with f(u)/u increasing for u gt; 0 and f(u) grows at ∞ faster than any power up (p gt; 1). As a distinct feature of this study appears the asymptotic behaviour of the boundary blow-up solution, which breaks up depending on how b(x) vanishes on ∂ω and how fast f grows at ∞.

    Original languageEnglish
    Pages (from-to)995-1030
    Number of pages36
    JournalAdvances in Differential Equations
    Volume12
    Issue number9
    Publication statusPublished - 2007

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