Abstract
The orbital stability of standing waves of nonlinear Schrödinger equations with a general nonlinear term is investigated in this paper. We study the corresponding minimizing problem with L 2-constraint:
We discuss when a minimizing sequence with respect to E α is precompact. We prove that there exists α 0 ≥ 0 such that there exists a global minimizer if α > α 0 and there exists no global minimizer if α < α 0. Moreover, some almost critical conditions which determine α 0 = 0 or α 0 > 0 are established, and the existence results with respect to \({E_{\alpha_0}}\) under some conditions are obtained.
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Shibata, M. Stable standing waves of nonlinear Schrödinger equations with a general nonlinear term. manuscripta math. 143, 221–237 (2014). https://doi.org/10.1007/s00229-013-0627-9
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DOI: https://doi.org/10.1007/s00229-013-0627-9