We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Fast and slow decay solutions for supercritical elliptic problems in exterior domains.
- Authors
Dávila, Juan; del Pino, Manuel; Musso, Monica; Juncheng Wei
- Abstract
We consider the elliptic problem Δ u + u p = 0, u > 0 in an exterior domain, $${\Omega = \mathbb{R}^N{\setminus}\mathcal{D}}$$ under zero Dirichlet and vanishing conditions, where $${\mathcal{D}}$$ is smooth and bounded in $${\mathbb{R}^N}$$ , N ≥ 3, and p is supercritical, namely $${p > \frac{N+2}{N-2}}$$ . We prove that this problem has infinitely many solutions with slow decay $${O(|x|^{-\frac2{p-1}})}$$ at infinity. In addition, a solution with fast decay O(| x|2- N ) exists if p is close enough from above to the critical exponent.
- Subjects
ELLIPTIC functions; FUNCTIONAL analysis; DYNAMICS; STATICS; MATHEMATICAL analysis; ANALYTICAL mechanics
- Publication
Calculus of Variations & Partial Differential Equations, 2008, Vol 32, Issue 4, p453
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-007-0154-1