Affiliation:
1. Department of Mathematics, Kyoto University, Kyoto 606-8502, JAPAN
Abstract
Abstract
We study the existence and stability of standing wave for the Schrödinger-Poisson-Slater equation in three dimensional space. Let p be the exponent of the nonlinear term. Then we first show that standing wave exists for 1 < p < 5. Next, we show that when 1 < p < 7/3 and p ≠ 2, standing wave is stable for some ω > 0. We also show that when 7/3 < p < 5, standing wave is unstable for some ω > 0. Furthermore, we investigate the case of p = 2. We prove these results by using variational methods.
Subject
General Mathematics,Statistical and Nonlinear Physics
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