Positive Solutions of a Semilinear Elliptic Equation with Singular Dirichlet Boundary Data

2015 ◽  
Vol 1 (2) ◽  
pp. 335-362
Author(s):  
Marek Fila ◽  
Kazuhiro Ishige ◽  
Tatsuki Kawakami
Keyword(s):  
Elliptic Equation ◽  
Positive Solutions ◽  
Boundary Data ◽  
Dirichlet Boundary ◽  
Semilinear Elliptic Equation ◽  
Semilinear Elliptic ◽  
Dirichlet Boundary Data

Multiple positive solutions for an unbounded Dirichlet boundary problem involving sign-changing weight

2009 ◽  
Vol 139 (6) ◽  
pp. 1297-1325
Author(s):  
Tsung-fang Wu
Keyword(s):  
Elliptic Equation ◽  
Positive Solutions ◽  
Dirichlet Boundary ◽  
Semilinear Elliptic Equation ◽  
Infinite Strip ◽  
Multiple Positive Solutions ◽  
Semilinear Elliptic ◽  
Multiplicity Of Positive Solutions ◽  
Image Position ◽  
Dirichlet Boundary Problem

We study the multiplicity of positive solutions for the following semilinear elliptic equation:where 1 < q < 2 < p < 2* (2* = 2N/(N − 2) if N ≥ 3, 2* = ∞ if N = 2), the parameters λ, μ ≥ 0, is an infinite strip in ℝN and Θ is a bounded domain in ℝN−1 We assume that fλ(x) = λf+(x) + f−(x) and gμ(x) = a(x) + μb(x), where the functions f±, a and b satisfy suitable conditions.

A Note on Symmetry of Solutions for a Class of Singular Semilinear Elliptic Problems

2016 ◽  
Vol 16 (3) ◽  
Author(s):  
Alessandro Trombetta
Keyword(s):  
Elliptic Equation ◽  
Dirichlet Boundary ◽  
Semilinear Elliptic Equation ◽  
Dirichlet Boundary Conditions ◽  
Moving Plane Method ◽  
Plane Method ◽  
Semilinear Elliptic ◽  
Moving Plane ◽  
Semilinear Elliptic Problems ◽  
Bounded Smooth

AbstractWe prove symmetry and monotonicity properties for positive solutions of the singular semilinear elliptic equationin bounded smooth domains with zero Dirichlet boundary conditions. The well-known moving plane method is applied.

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