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Solitary solutions for a class of Schrödinger equations in \({\mathbb{R}^3}\)

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Abstract

In this paper, we consider a model problem arising from a classical planar Heisenberg ferromagnetic spin chain

$$-\Delta u + (\lambda + \varepsilon') u \mp \Delta \sqrt{1-u^{2}}\frac{u}{\sqrt{1- u^{2}}} - \varepsilon'\frac{u}{\sqrt{1 - u^{2}}} = 0, \, x \in \mathbb{R}^{3},$$

where \({\lambda}\) and \({\varepsilon'}\)are real constants. By variational methods and perturbation arguments, we study the existence of positive classical solutions. Our results generalize the previous results in one-dimensional space given by Brüll et al. [4].

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Authors and Affiliations

  1. School of Mathematics, South China University of Technology, Guangzhou, 510640, People’s Republic of China

    Youjun Wang

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  1. Youjun Wang
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Correspondence to Youjun Wang.

Additional information

Supported by NSFC (No. 11201154) and the Fundamental Research Funds for the Central Universities (No. 2014ZZ0065).

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Wang, Y. Solitary solutions for a class of Schrödinger equations in \({\mathbb{R}^3}\) . Z. Angew. Math. Phys. 67, 88 (2016). https://doi.org/10.1007/s00033-016-0679-2

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  • DOI: https://doi.org/10.1007/s00033-016-0679-2

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