Blow-up solutions with minimal mass for nonlinear Schrödinger equation with variable potential
This paper studies the mass-critical variable coefficient nonlinear Schrödinger equation. We first get the existence of the ground state by solving a minimization problem. Then we prove a compactness result by the variational characterization of the ground state solutions. In addition, we construct...
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| Main Authors: | , |
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| Format: | article |
| Language: | EN |
| Published: |
De Gruyter
2021
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| Subjects: | |
| Online Access: | https://doaj.org/article/50f43f151ff94a1a846067da8b374f1b |
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| Summary: | This paper studies the mass-critical variable coefficient nonlinear Schrödinger equation. We first get the existence of the ground state by solving a minimization problem. Then we prove a compactness result by the variational characterization of the ground state solutions. In addition, we construct the blow-up solutions at the minimal mass threshold and further prove the uniqueness result on the minimal mass blow-up solutions which are pseudo-conformal transformation of the ground states. |
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