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Multiple positive solutions for Schrödinger systems with mixed couplings

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Abstract

We study the effects of mixed couplings for nonlinear Schrödinger systems. We show due to the mixed couplings there exist multiple vector positive solutions which exhibit interesting new patterns of co-existence of synchronization and segregation. For a 3-system we show the existence of multiple positive vector solutions with the first two components being synchronized and segregated from the third component. We investigate the asymptotic of these solutions with a large attractive coupling constant.

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Acknowledgments

The authors are grateful to the referee for a thoughtful reading of the manuscript and for several helpful suggestions. The first author is partially supported by the JSPS Strategic Young Researcher Overseas Visits Program for Accelerating Brain Circulation “Deepening and Evolution of Mathematics and Physics, Building of International Network Hub based on OCAMI”. The second author is supported by NSFC11271201.

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Authors and Affiliations

  1. Department of Mathematics, Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama-shi, 338-8570, Japan

    Yohei Sato

  2. Advanced Mathematical Institute, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Smiyoshi-ku, Osaka, 558-8585, Japan

    Yohei Sato

  3. Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China

    Zhi-Qiang Wang

  4. Department of Mathematics and Statistics, Utah State University, Logan, UT, 84322, USA

    Zhi-Qiang Wang

Authors
  1. Yohei Sato
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  2. Zhi-Qiang Wang
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Correspondence to Yohei Sato.

Additional information

Communicated by P. Rabinowitz.

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Sato, Y., Wang, ZQ. Multiple positive solutions for Schrödinger systems with mixed couplings. Calc. Var. 54, 1373–1392 (2015). https://doi.org/10.1007/s00526-015-0828-z

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  • DOI: https://doi.org/10.1007/s00526-015-0828-z

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