Abstract
For k = 1, · · ·, K, let Mk be a qk-dimensional smooth compact framed manifold in ℝN with qk ∈ {1, · · ·, N - 1}. We consider the equation -ε2Δu + V(x)u - up = 0 in ℝN where for each k ∈ {1, · · ·, K} and some mk > 0, V(x) = |dist(x, Mk)|mk + O(|dist(x, Mk)|mk+1) as dist(x, Mk) → 0. For a sequence of ε converging to zero, we will find a positive solution uε of the equation which concentrates on M1 ∪ · · · ∪ MK.
Original language | English |
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Pages (from-to) | 825-842 |
Number of pages | 18 |
Journal | Communications on Pure and Applied Analysis |
Volume | 14 |
Issue number | 3 |
DOIs | |
Publication status | Published - May 1 2015 |
Keywords
- Concentration phenomena
- Infinite dimensional reduction
- Nondegeneracy
- Nonlinear schrdinger equation
ASJC Scopus subject areas
- Analysis
- Applied Mathematics