Isolated singularities of some semilinear elliptic equations
نویسندگان
چکیده
منابع مشابه
Singular Solutions for some Semilinear Elliptic Equations
We are concerned with the behavior of u near x = O. There are two distinct cases: 1) When p >= N / ( N -2) and (N ~ 3) it has been shown by BR~ZIS & V~RON [9] that u must be smooth at 0 (See also BARAS & PIERRE [1] for a different proof). In other words, isolated singularities are removable. 2) When 1-< p < N / ( N 2) there are solutions of (1) with a singularity at x ---0. Moreover all singula...
متن کاملSome Limiting Situations for Semilinear Elliptic Equations
— The objective of this mini-course is to take a look at a standard semilinear partial differential equation −∆u = λf(u) on which we show the use of some basic tools in the study of elliptic equation. We will mention the maximum principle, barrier method, blow-up analysis, regularity and boot-strap argument, stability, localization and quantification of singularities, Pohozaev identities, movin...
متن کاملConformally invariant fully nonlinear elliptic equations and isolated singularities
1 Introduction There has been much work on conformally invariant fully nonlinear elliptic equations and applications to geometry and topology. [10], and the references therein. In this and a companion paper [16] we address some analytical issues concerning these equations. For n ≥ 3, consider −∆u = n − 2 2 u n+2 n−2 , on R n .
متن کاملMultiple Nontrivial Solutions of Elliptic Semilinear Equations
We find multiple solutions for semilinear boundary value problems when the corresponding functional exhibits local splitting at zero.
متن کاملGeometrization Program of Semilinear Elliptic Equations
Understanding the entire solutions of nonlinear elliptic equations in RN such as (0.1) Δu+ f(u) = 0 in R , is a basic problem in PDE research. This is the context of various classical results in literature like the Gidas-Ni-Nirenberg theorems on radial symmetry, Liouville type theorems, or the achievements around De Giorgi’s conjecture. In those results, the geometry of level sets of the soluti...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1985
ISSN: 0022-0396
DOI: 10.1016/0022-0396(85)90127-5