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On semilinear elliptic equations with indefinite nonlinearities [PDF]

Calculus of Variations and Partial Differential Equations, 1993
Abstract: "This paper concerns semilinear elliptic equations whose nonlinear term has the form W(x)f(u) where W changes sign. We study the existence of positive solutions and their multiplicity. The important role played by the negative part of W is contained in a condition which is shown to be necessary for homogeneous f.
Gabriella Tarantello, Stanley Alama
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Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth

, 1989
On etudie les solutions regulieres non negatives de l'equation conformement invariante −Δu=u (n+2)/(n−2) , u>0 dans une boule perforee, B 1 (0)\{0}⊂R n , n≥3, avec une singularite isolee a l ...
L. Caffarelli, B. Gidas, J. Spruck
semanticscholar   +1 more source

Symmetrization for singular semilinear elliptic equations

Annali di Matematica Pura ed Applicata, 2012
In this paper, we prove some comparison results for the solution to a Dirichlet problem associated with a singular elliptic equation and we study how the summability of such a solution varies depending on the summability of the datum f.
BRANDOLINI, BARBARA, CHIACCHIO, FRANCESCO, TROMBETTI, CRISTINA   +2 more
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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(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.
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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
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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
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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
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On the classification of solutions of a semilinear elliptic equation

Nonlinear Analysis: Theory, Methods & Applications, 1991
The authors consider the structure of the set of all positive solutions of the equation \(\Delta u+K(x)u^ \sigma=0\) in \(\mathbb{R}^ 2\), where \(\sigma>1\) is a constant. The structure of the solution set in \(\mathbb{R}^ 2\) is quite different from that of the case in \(\mathbb{R}^ n\), \(n\geq 3\). Main problems investigated are on the existence of
Jenn-Nan Wang, Kuo-Shung Cheng
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A class of semilinear elliptic equations on groups of polynomial growth

Journal of Differential Equations, 2023
B. Hua, Ruo Li, Lidan Wang
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Semilinear elliptic equations with singular nonlinearities

Calculus of Variations and Partial Differential Equations, 2009
We prove existence, regularity and nonexistence results for problems whose model is $$-\Delta u = \frac{f(x)}{u^{\gamma}}\quad {{\rm in}\,\Omega},$$ with zero Dirichlet conditions on the boundary of an open, bounded subset Ω of \({\mathbb{R}^{N}}\). Here γ > 0 and f is a nonnegative function on Ω.
BOCCARDO, Lucio, ORSINA, Luigi
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