Entire solutions with asymptotic self-similarity for elliptic equations with exponential nonlinearity
نویسندگان
چکیده
منابع مشابه
Asymptotic Behavior of Blowup Solutions for Elliptic Equations with Exponential Nonlinearity and Singular Data
We consider a sequence of blowup solutions of a two dimensional, second order elliptic equation with exponential nonlinearity and singular data. This equation has a rich background in physics and geometry. In a work of Bartolucci-Chen-Lin-Tarantello it is proved that the profile of the solutions differs from global solutions of a Liouville type equation only by a uniformly bounded term. The pre...
متن کاملSolutions of Semilinear Elliptic Equations with Asymptotic Linear Nonlinearity
In this paper, we consider some semilinear elliptic equations with asymptotic linear nonlinearity and show the existence, uniqueness, and asymptotic behavior of these solutions.
متن کاملEntire Solutions for a Semilinear Fourth Order Elliptic Problem with Exponential Nonlinearity∗
We investigate entire radial solutions of the semilinear biharmonic equation ∆u = λ exp(u) in Rn, n ≥ 5, λ > 0 being a parameter. We show that singular radial solutions of the corresponding Dirichlet problem in the unit ball cannot be extended as solutions of the equation to the whole of Rn. In particular, they cannot be expanded as power series in the natural variable s = log |x|. Next, we pro...
متن کاملAsymptotic Spatial Patterns and Entire Solutions of Semilinear Elliptic Equations
(2) ε∆uε + f(uε) = 0, x ∈ Ω, Bu = 0, x ∈ ∂Ω, where ε > 0 is a small parameter, Ω is a smooth bounded domain in Rn, and Bu is an appropriate boundary condition. The connection of (1) and (2) are made by a typical technique called blowup method. Suppose that {uε} is a family of solutions of (2). The simplest setup of the blowup method is to choose Pε ∈ Ω, and define vε(y) = uε(εy + Pε), for y ∈ Ω...
متن کاملPositive Solutions for Elliptic Equations with Singular Nonlinearity
We study an elliptic boundary-value problem with singular nonlinearity via the method of monotone iteration scheme: −∆u(x) = f(x, u(x)), x ∈ Ω, u(x) = φ(x), x ∈ ∂Ω, where ∆ is the Laplacian operator, Ω is a bounded domain in RN , N ≥ 2, φ ≥ 0 may take the value 0 on ∂Ω, and f(x, s) is possibly singular near s = 0. We prove the existence and the uniqueness of positive solutions under a set of hy...
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 Mathematical Analysis and Applications
سال: 2015
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2015.03.036