1 results
Nodal vector solutions with clustered peaks for nonlinear elliptic equations in ℝ3
- Part of
-
- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 146 / Issue 5 / October 2016
- Published online by Cambridge University Press:
- 01 July 2016, pp. 947-982
- Print publication:
- October 2016
-
- Article
- Export citation
-
We study the following coupled nonlinear Schr¨odinger system in ℝ3:
where μ1 > 0, μ2 > 0 and β ∈ ℝ is a coupling constant. Irrespective of whether the system is repulsive or attractive, we prove that it has nodal semi-classical segregated or synchronized bound states with clustered spikes for sufficiently small ε under some additional conditions on P(x), Q(x) and β. Moreover, the number of this type of solutions will go to infinity as ε → 0+.
