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Ground State Solutions for Resonant Cooperative Elliptic Systems with General Superlinear Terms

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Abstract

This paper is concerned with the following cooperative elliptic system:

$$\left\{ \begin{array}{ll} -\Delta u=\xi u+f(x,u,v), \quad \quad \mbox{in } \Omega, -\Delta v=\zeta v+g(x,u,v), \quad \quad \mbox{in } \Omega, u=v=0, \quad \quad\mbox{on } \partial\Omega, \end{array} \right.$$

where \({U=(u,v): \Omega\rightarrow \mathbb{R}^{2}}\), Ω is a bounded smooth domain in \({\mathbb{R}^{N}}\) and \({\xi,\zeta\in\mathbb{R}}\). We establish the existence of ground state solutions for this system using a much more direct approach to find a minimizing Cerami sequence for the energy functional outside the generalized Nehari manifold developed recently by Szulkin and Weth.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, Hunan, People’s Republic of China

    Hongxia Shi & Haibo Chen

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  1. Hongxia Shi
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  2. Haibo Chen
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Correspondence to Haibo Chen.

Additional information

This research was supported by Natural Science Foundation of China 11271372, by the Fundamental Research Funds for the Central Universities of Central South University 2015zzts010 and by the Mathematics and Interdisciplinary Sciences project of CSU.

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Shi, H., Chen, H. Ground State Solutions for Resonant Cooperative Elliptic Systems with General Superlinear Terms. Mediterr. J. Math. 13, 2897–2909 (2016). https://doi.org/10.1007/s00009-015-0663-7

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  • DOI: https://doi.org/10.1007/s00009-015-0663-7

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