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On the existence and regularity of vector solutions for quasilinear systems with linear coupling

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Abstract

We study the following coupled system of quasilinear equations:

$$\begin{cases}-\Delta_pu+|u|^{p-2}u=f(u)+\lambda v, & x \in \mathbb{R}^N,\\-\Delta_pv+|v|^{p-2}v=g(v)+\lambda u, & x \in \mathbb{R}^N.\end{cases}$$

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Under some assumptions on the nonlinear terms f and g, we establish some results about the existence and regularity of vector solutions for the p-Laplacian systems by using variational methods. In particular, we get two pairs of nontrivial solutions. We also study the different asymptotic behavior of solutions as the coupling parameter λ tends to zero.

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Authors and Affiliations

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

    Yong Ao, Jiaqi Wang & Wenming Zou

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  1. Yong Ao
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  2. Jiaqi Wang
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  3. Wenming Zou
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Correspondence to Wenming Zou.

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Ao, Y., Wang, J. & Zou, W. On the existence and regularity of vector solutions for quasilinear systems with linear coupling. Sci. China Math. 62, 125–146 (2019). https://doi.org/10.1007/s11425-017-9235-2

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