The singular set of stationary solution for semilinear elliptic equations with supercritical growth
نویسندگان
چکیده
منابع مشابه
Bubble towers for supercritical semilinear elliptic equations
Abstract : We construct positive solutions of the semilinear elliptic problem ∆u + λu + up = 0 with Dirichet boundary conditions, in a bounded smooth domain Ω ⊂ RN (N ≥ 4), when the exponent p is supercritical and close enough to N+2 N−2 and the parameter λ ∈ R is small enough. As p → N+2 N−2 , the solutions have multiple blow up at finitely many points which are the critical points of a functi...
متن کاملSingular 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 کاملStructure of the solution set for a class of semilinear elliptic equations with asymptotic linear nonlinearity
We consider a semilinear elliptic equation with asymptotic linear nonlinearity applying bifurcation theory and spectral analysis. We obtain the exact multiplicity of the positive solutions and a very precise structure of the solution set, which improves the previous knowledge of the problem.
متن کاملNon-existence and uniqueness results for supercritical semilinear elliptic equations
Non-existence and uniqueness results are proved for several local and non-local supercritical bifurcation problems involving a semilinear elliptic equation depending on a parameter. The domain is star-shaped and such that a Poincaré inequality holds but no other symmetry assumption is required. Uniqueness holds when the bifurcation parameter is in a certain range. Our approach can be seen, in s...
متن کاملExistence of Positive Weak Solutions with a Prescribed Singular Set of Semilinear Elliptic Equations
In this paper, we consider the problem of the existence of non-negative weak solution u of A u + u P = O i n ~ u = 0 on Of~ n n + 2 ~ / n 1 having a given closed set S as its singular set. We prove that when < p < _ _ and n 2 n 4 + 2 nv/'n-L--1 S is a closed subset of f2, then there are infinite many positive weak solutions with S as their singular set. Applying this method to the conformal sca...
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: 2014
ISSN: 0022-0396
DOI: 10.1016/j.jde.2014.01.006