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The critical case for a Berestycki-Lions theorem

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Abstract

We consider the existence of the ground states solutions to the following Schrödinger equation:

$$- \Delta u + V(x)u = f(u), u \in H^1 \left( {\mathbb{R}^N } \right),$$

where N ⩾ 3 and f has critical growth. We generalize an earlier theorem due to Berestycki and Lions about the subcritical case to the current critical case.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Jian Zhang & WenMing Zou

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  1. Jian Zhang
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  2. WenMing Zou
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Correspondence to WenMing Zou.

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Zhang, J., Zou, W. The critical case for a Berestycki-Lions theorem. Sci. China Math. 57, 541–554 (2014). https://doi.org/10.1007/s11425-013-4687-9

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  • DOI: https://doi.org/10.1007/s11425-013-4687-9

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