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 |
|---|---|
| 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
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Byeon, J., Kwon, O., & Oshita, Y. (2015). Standing wave concentrating on compact manifolds for nonlinear Schrödinger equations. Communications on Pure and Applied Analysis, 14(3), 825-842. https://doi.org/10.3934/cpaa.2015.14.825