Locations of spikes for linearly coupled Schrodinger systems

In this paper, we consider the following Schrodinger system with linearly coupled terms: {-epsilon(2)Delta u + u = vertical bar u vertical bar(2)u + lambda v in Omega, (A(1)) -epsilon(2)Delta v + v = vertical bar v vertical bar(2)v + lambda u in Omega, where epsilon > 0, 0 < lambda < 1, and Omega is a bounded smooth domain in Double-struck capital R-3. Under the Dirichlet or Neumann boundary conditions, we study the locations and interaction of spikes for ground states of (A1) by the variation method, maximum principle, and blow up technique.

Automated summary

This paper investigates the locations and interaction of spikes for the ground states of a Schrodinger system with linearly coupled terms under Dirichlet or Neumann boundary conditions, utilizing the variation method, maximum principle, and blow up technique.