Singular variation of the ground state eigenvalue for a semilinear elliptic equation
نویسندگان
چکیده
منابع مشابه
A two-phase free boundary problem for a semilinear elliptic equation
In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary. We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...
متن کاملExistence of ground state solutions for a class of nonlinear elliptic equations with fast increasing weight
This paper is devoted to get a ground state solution for a class of nonlinear elliptic equations with fast increasing weight. We apply the variational methods to prove the existence of ground state solution.
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 کاملA construction of singular solutions for a semilinear elliptic equation using asymptotic analysis
The aim of this paper is to prove the existence of weak solutions to the equation ∆u+u = 0 which are positive in a domain Ω ⊂ R , vanish at the boundary, and have prescribed isolated singularities. The exponent p is required to lie in the interval (N/(N − 2), (N + 2)/(N − 2)). We also prove the existence of solutions to the equation ∆u+ u = 0 which are positive in a domain Ω ⊂ R and which are s...
متن کاملOn a singular nonlinear semilinear elliptic problem
where K(x)μC2,b(V9 ), a, pμ(0, 1) and l is a real parameter. Such singular elliptic problems arise in the contexts of chemical heterogeneous catalysts, nonNewtonian fluids and also the theory of heat conduction in electrically conducting materials, see [3, 5, 8, 9] for a detailed discussion. Obviously (1.1) cannot have a solution uμC2(V9 ) if K(x) is not vanishing near ∂V. However, under variou...
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: Tohoku Mathematical Journal
سال: 1993
ISSN: 0040-8735
DOI: 10.2748/tmj/1178225889