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Orbital Stability of Standing Waves for the Sobolev Critical Schrödinger Equation with Inverse-Power Potential

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Abstract

In this paper, we study the Cauchy problem for the nonlinear Schrödinger equation with focusing inverse-power potential and the Sobolev critical nonlinearity. By considering the corresponding local minimization problem, we show that the existence of ground state solutions. Then, we prove that the solution of this equation exists globally when the initial data \(\varphi \) sufficiently close to the ground states. Based on these results, we show that the set of ground states is orbitally stable.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 12261079), and the Outstanding Youth Science Fund of Gansu Province (No. 20JR10RA111).

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Authors and Affiliations

  1. Department of Mathematics, Northwest Normal University, Lanzhou, 730070, China

    Leijin Cao & Binhua Feng

  2. Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, 730070, China

    Yichun Mo

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  1. Leijin Cao
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  2. Binhua Feng
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  3. Yichun Mo
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Correspondence to Leijin Cao.

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Cao, L., Feng, B. & Mo, Y. Orbital Stability of Standing Waves for the Sobolev Critical Schrödinger Equation with Inverse-Power Potential. Qual. Theory Dyn. Syst. 23, 147 (2024). https://doi.org/10.1007/s12346-024-00980-7

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