Bubbling solutions for an exponential nonlinearity inR2
نویسندگان
چکیده
منابع مشابه
Stable Solutions for the Bilaplacian with Exponential Nonlinearity
Let λ > 0 denote the largest possible value of λ such that
متن کاملThe singular extremal solutions of the bilaplacian with exponential nonlinearity
Consider the problem ∆u = λe in B u = ∂u ∂n = 0 on ∂B, where B is the unit ball in R and λ is a parameter. Unlike the Gelfand problem the natural candidate u = −4 ln(|x|), for the extremal solution, does not satisfy the boundary conditions and hence showing the singular nature of the extremal solution in large dimensions close to the critical dimension is challenging. Dávila et al. in [5] use...
متن کاملBubbling Solutions for an Anisotropic Emden-Fowler Equation
We consider the following anisotropic Emden-Fowler equation ∇(a(x)∇u) + εa(x)e = 0 in Ω, u = 0 on ∂Ω where Ω ⊂ R is a bounded smooth domain and a(x) is a positive smooth function. We investigate the effect of anisotropic coefficient a(x) on the existence of bubbling solutions. We show that at given local maximum points of a(x), there exists arbitrarily many bubbles. As a consequence, the quanti...
متن کاملThe Two-dimensional Lazer-mckenna Conjecture for an Exponential Nonlinearity
where Ω is a bounded, smooth domain in R, φ1 is a positive first eigenfunction of the Laplacian under Dirichlet boundary conditions and h ∈ C(Ω̄). We prove that given k ≥ 1 this problem has at least k solutions for all sufficiently large s > 0, which answers affirmatively a conjecture by Lazer and McKenna [22] for this case. The solutions found exhibit multiple concentration behavior around maxi...
متن کاملBubbling solutions for supercritical problems on manifolds
Article history: Received 15 May 2014 Available online 10 November 2014 MSC: 35B10 35B33 35J08 58J05
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.2014.05.034