Asymptotic behavior of positive solutions of a semilinear Dirichlet problem in exterior domains
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In this article, we study the existence, uniqueness and the asymptotic behavior of a positive classical solution to the semilinear boundary-value problem -∆u = α(x)uσ in D, u|∂D = 0, lim|x|→∞ u(x) = 0. Here D is an unbounded regular domain in ℝn (n ≥ 3) with compact boundary, σ < 1 and the function α is a nonnegative function in C γ loc (D), 0 < γ < 1, satisfying an appropriate assumption related to Karamata regular variation theory.
CitationMâagli, H., Alzahrani, A. K., & Zine El Abidine, Z. (2018). Asymptotic behavior of positive solutions of a semilinear Dirichlet problem in exterior domains. Electronic Journal of Differential Equations, 2018(137), pp. 1-14.
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