Asymptotic behavior of positive solutions of a semilinear Dirichlet problem in exterior domains
Date
2018-07-01
Authors
Maagli, Habib
Alzahrani, Abdulah Khamis
Zine El Abidine, Zagharide
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
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.
Description
Keywords
Positive solutions, Asymptotic behavior, Dirichlet problem, Subsolution, Supersolution
Citation
Mâagli, H., Alzahrani, A. K., & Zine El Abidine, Z. (2018). Asymptotic behavior of positive solutions of a semilinear Dirichlet problem in exterior domains. <i>Electronic Journal of Differential Equations, 2018</i>(137), pp. 1-14.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.