On ground state solutions for superlinear Hamiltonian elliptic systems |
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Authors: | Leiga Zhao Fukun Zhao |
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Institution: | 1. Department of Mathematics, Beijing University of Chemical Technology, Beijing, 100029, People’s Republic of China 2. Department of Mathematics, Yunnan Normal University, Kunming, 650092, People’s Republic of China
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Abstract: | In this paper, we study the following Hamiltonian elliptic systems $$\left\{\begin{array}{ll}-\Delta u+V(x)u= g(x,v),\quad {\rm in }\, \mathbb{R}^N,\\-\Delta v+V(x)v= f(x,u),\quad {\rm in } \, \mathbb{R}^N.\end{array}\right.$$ where ${V(x)\in C(\mathbb R^N), f(x,t), g(x,t)\in C(\mathbb{R}^N\times \mathbb{R})}$ are superlinear in t at infinity. Without Ambrosetti–Rabinowtitz condition, the existences of ground state solutions are obtained via the combination of generalized linking theorem and monotonicity method. |
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