Results 241 to 250 of about 93,033 (295)

Uniqueness of continuation for semilinear elliptic equations

Partial Differential Equations and Applications, 2022
We quantify the uniqueness of continuation from Cauchy or interior data. Our approach consists in extending the existing results in the linear case. As by product, we obtain a new stability estimate in the linear case.
M. Choulli
semanticscholar   +1 more source

G-convergence and semilinear elliptic equations

Asymptotic Analysis, 1991
We study the behavior of positive solutions of semilinear elliptic equations −div(aε(x)Duε=g(uε) with homogeneous Dirichlet boundary data, with respect to the G-convergence of the elliptic matrices aε. Here the function g has a subcritical or critical growth with respect to Sobolev imbedding.
DALL'AGLIO, Andrea, TCHOU N. A.
openaire   +3 more sources

On some Semilinear Elliptic Equations

AIP Conference Proceedings, 2009
In this paper we study the third type boundary value problem for a Semilinear Elliptic Equation. Here the existence of the weak solution for the considered problem is proved and also the uniqueness of the solution of the considered problem, in a model case, is proved.
Kerime Kalli, Kamal N. Soltanov, Theodore E. Simos, George Psihoyios, Ch. Tsitouras   +4 more
openaire   +1 more source

Asymptotic Theory of Singular Semilinear Elliptic Equations

Canadian Mathematical Bulletin, 1984
AbstractNecessary and sufficient conditions are found for the existence of two positive solutions of the semilinear elliptic equation Δu + q(|x|)u = f(x, u) in an exterior domain Ω⊂ℝn, n ≥ 1, where q, f are real-valued and locally Hölder continuous, and f(x, u) is nonincreasing in u for each fixed x∈Ω. An example is the singular stationary Klein-Gordon
Kusano, Takasi, Swanson, Charles A.
openaire   +2 more sources

Singular Solutions for some Semilinear Elliptic Equations

Archive for Rational Mechanics and Analysis, 1987
This paper studies solutions \(u\in C\) \(2(B_ R\setminus 0)\) of the equation \(-\Delta u+u\) \(p=0\), \(u\geq 0\) on \(B_ R\setminus 0\), the dimension of the underlying space being N.
Brézis, Haïm, Oswald, Luc
openaire   +1 more source

An Adaptive Multigrid Method for Semilinear Elliptic Equations

East Asian Journal on Applied Mathematics, 2019
An adaptive multigrid method for semilinear elliptic equations based on adaptive multigrid methods and on multilevel correction methods is developed.
Fei Xu, Qiumei Huang, Shuangshuang Chen, Tao Bing   +3 more
semanticscholar   +1 more source

Global Positive Solutions of Semilinear Elliptic Equations

Canadian Journal of Mathematics, 1983
The semilinear elliptic boundary value problem1.1will be considered in an exterior domain Ω ⊂ Rn, n ≥ 2, with boundary ∂Ω ∊ C2 + α, 0 < α < 1, where1.2Di = ∂/∂xi, i = 1, …, n. The coefficients aij, bi in (1.2) are assumed to be real-valued functions defined in Ω ∪ ∂Ω such that each , , and (aij(x)) is uniformly positive definite in every bounded ...
Noussair, Ezzat S., Swanson, Charles A.
openaire   +1 more source

Nonexistence of positive supersolutions to a class of semilinear elliptic equations and systems in an exterior domain

Science China Mathematics, 2018
In this paper, we consider the following semilinear elliptic equation: {−Δu=h(x,u)inΩ,u⩾0on∂Ω,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs ...
Huyuan Chen, Rui Peng, F. Zhou
semanticscholar   +1 more source

Symmetrization for singular semilinear elliptic equations

Annali di Matematica Pura ed Applicata, 2012
The authors are interested in the following semi-linear Dirichlet problem: \[ -\Delta u=\frac{f(x)}{u^\gamma}\text{ and }u>0\text{ in }G,\quad u=0\text{ on }\partial G, \] where \(G \subset \mathbb{R}^n\) is a bounded domain, \(\gamma\) is a positive constant and \(f\) is a positive function. First the authors define the notion of a weak solution under
BRANDOLINI, BARBARA, CHIACCHIO, FRANCESCO, TROMBETTI, CRISTINA   +2 more
openaire   +4 more sources

A class of semilinear elliptic equations on groups of polynomial growth

Journal of Differential Equations, 2023
B. Hua, Ruo Li, Lidan Wang
semanticscholar   +1 more source