Positive Solutions of Nonlinear Elliptic Equations in a Half Space in R2
Date
2002-05-16
Authors
Bachar, Imed
Maagli, Habib
Maatoug, Lamia
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We study the existence and the asymptotic behaviour of positive solutions of the nonlinear equation Δu + ƒ(., u) = 0, in the domain D = {(x1, x2) ∈ ℝ2 : x2 > 0}, with u = 0 on the boundary. The aim is to prove some existence results for the above equation in a general setting by using a fixed-point argument.
Description
Keywords
Singular elliptic equation, Superharmonic function, Green function, Schauder fixed point theorem, Maximum principle
Citation
Bachar, I., Maagli, H., & Maatoug, L. (2002). Positive solutions of nonlinear elliptic equations in a half space in R2. Electronic Journal of Differential Equations, 2002(41), pp. 1-24.
Rights
Attribution 4.0 International