Partially concentrating standing waves for weakly coupled Schrödinger systems

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2024年3月29日

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Benedetta Pellacci,
Angela Pistoia,
Giusi Vaira,
Gianmaria Verzini

摘要

We study the existence of standing waves for the following weakly coupled system of two Schrödinger equations where $V_1$ $V_{1}$ and $V_2$ $V_{2}$ are radial potentials bounded from below. We address the case , $m_2$ $m_{2}$ constant, and prove the existence of a standing wave solution with both nontrivial components satisfying a prescribed asymptotic profile. In particular, the second component of such solution exhibits a concentrating behavior, while the first one keeps a quantum nature.