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ADAPTIVE FINITE ELEMENT MODELING TECHNIQUES FOR THE POISSON-BOLTZMANN EQUATION. [PDF]

open access: yesCommun Comput Phys, 2012
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Semilinear Elliptic Equations with Singularity on the Boundary

Journal of Partial Differential Equations, 2002
In this paper, we consider the existence and nonexistence of positive solutions to semilinear elliptic equation -Δu = K(x)(1-|x|)^{-λ_u^q} in the unit ball B with 0-Dirichlet boundary condition. Our main tools are based on the interior estimates of the Schauder type, the Schauder fixed point theorem and the pointwise estimates for Green functions.
Zeng, Youdong, Chen, Zuchi
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G-convergence and semilinear elliptic equations

Asymptotic Analysis, 1991
We study the behavior of positive solutions of semilinear elliptic equations −div(a ε (x)Du ε =g(u ε ) with homogeneous Dirichlet boundary data, with respect to the G-convergence of the elliptic matrices a
DALL'AGLIO, Andrea, TCHOU N. A.
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Asymptotic properties of semilinear elliptic equations

Funkcialaj Ekvacioj, 1983
Semilinear elliptic equations of the type (1) \(\Delta u+f(x,u)=0\) are considered in exterior domains \(\Omega \subset {\mathbb{R}}^ n\), \(n\geq 2\), where \(\Delta\) denotes the n-dimensional Laplacian and f is locally Hölder continuous in \(\Omega \times {\mathbb{R}}^+\).
Kusano, Takaŝi, Swanson, A. Charles
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