Abstract
We prove sharp existence and nonexistence results for minimal energy solutions of the nonlinear Schrödinger system
in the cooperative and subcritical case \({b > 0, 1 < q < \frac{n}{(n-2)_+}}\) . The proofs are accomplished by minimizing the Euler functional of (1) over the two associated Nehari manifolds. In the special case \({1 < q < 2}\) we find that a positive solution of (1) with minimal energy among all nontrivial solutions exists if and only if b > 0.
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Mandel, R. Minimal energy solutions for cooperative nonlinear Schrödinger systems. Nonlinear Differ. Equ. Appl. 22, 239–262 (2015). https://doi.org/10.1007/s00030-014-0281-2
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DOI: https://doi.org/10.1007/s00030-014-0281-2