scholarly journals Boundedness of Stable Solutions to Semilinear Elliptic Equations: A Survey

2017 ◽  
Vol 17 (2) ◽  
Author(s):  
Xavier Cabré
Keyword(s):  
Elliptic Equations ◽  
Elliptic Problems ◽  
Semilinear Elliptic Equations ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic Problems ◽  
Stable Solutions

AbstractThis article is a survey on boundedness results for stable solutions to semilinear elliptic problems. For these solutions, we present the currently known

Existence and non-existence results for semilinear elliptic problems in unbounded domains

1982 ◽  
Vol 93 (1-2) ◽  
pp. 1-14 ◽  
Author(s):  
M. J. Esteban ◽  
P. L. Lions
Keyword(s):  
Elliptic Equations ◽  
Elliptic Problems ◽  
Unbounded Domains ◽  
Existence Results ◽  
Semilinear Elliptic Equations ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic Problems ◽  
Image Position

SynopsisIn this paper, we prove various existence and non-existence results for semilinear elliptic problems in unbounded domains. In particular we prove for general classes of unbounded domains that there exists no solution distinct from 0 offor any smooth f satisfying f(0) = 0. This result is obtained by the use of new identities that solutions of semilinear elliptic equations satisfy.

scholarly journals Positive Solutions for Elliptic Problems with the Nonlinearity Containing Singularity and Hardy-Sobolev Exponents

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yong-Yi Lan ◽  
Xian Hu ◽  
Bi-Yun Tang
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Elliptic Problems ◽  
Semilinear Elliptic Equations ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic ◽  
Multiplicity Of Positive Solutions

In this paper, we study multiplicity of positive solutions for a class of semilinear elliptic equations with the nonlinearity containing singularity and Hardy-Sobolev exponents. Using variational methods, we establish the existence and multiplicity of positive solutions for the problem.

Some results for semilinear elliptic equations with critical potential

2002 ◽  
Vol 132 (1) ◽  
pp. 1-24 ◽  
Author(s):  
B. Abdellaoui ◽  
I. Peral
Keyword(s):  
Elliptic Equations ◽  
Elliptic Problems ◽  
Semilinear Elliptic Equations ◽  
Critical Potential ◽  
Semilinear Elliptic ◽  
Image Position

This paper is devoted to the study of the elliptic problems with a critical potential, where N ≥ 3, λ ≥ 0 and 0 < q < 1 < p ≤ (N + 2)/(N − 2). Existence, multiplicity, behaviour in x = 0 and bifurcation are considered under some hypotheses in h and g.

scholarly journals Stable solutions to semilinear elliptic equations are smooth up to dimension $9$

2020 ◽  
Vol 224 (2) ◽  
pp. 187-252 ◽  
Author(s):  
Xavier Cabré ◽  
Alessio Figalli ◽  
Xavier Ros-Oton ◽  
Joaquim Serra
Keyword(s):  
Elliptic Equations ◽  
Semilinear Elliptic Equations ◽  
Semilinear Elliptic ◽  
Stable Solutions
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