Science China Mathematics

, Volume 62, Issue 1, pp 125–146 | Cite as

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

  • Yong Ao
  • Jiaqi Wang
  • Wenming ZouEmail author


We study the following coupled system of quasilinear equations:
$$\begin{cases}-\Delta_pu+|u|^{p-2}u=f(u)+\lambda v, & x \in \mathbb{R}^N,\\-\Delta_pv+|v|^{p-2}v=g(v)+\lambda u, & x \in \mathbb{R}^N.\end{cases}$$

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.


p-Laplacian system least energy solutions Moser iteration variational methods 


35B33 35J20 58E05 


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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingChina

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