Corrigendum to "Minimality of the horocycle flow on laminations by hyperbolic surfaces with non-trivial topology"
Measurable sensitivity via Furstenberg families
August 2017, 37(8): 4565-4583. doi: 10.3934/dcds.2017195
Ground state solutions for Hamiltonian elliptic system with inverse square potential
Jian Zhang 1, , Wen Zhang 1,, and Xianhua Tang 2,
School of Mathematics and Statistics, Hunan University of Commerce, Changsha, 410205 Hunan, China
School of Mathematics and Statistics, Central South University, Changsha, 410083 Hunan, China
Received October 2016 Revised February 2017 Published April 2017
Fund Project: This work was supported by the NNSF (Nos. 11601145,11571370,11471137), by the Natural Science Foundation of Hunan Province (Nos. 2017JJ3130,2017JJ3131), and by the Hunan University of Commerce Innovation Driven Project for Young Teacher (16QD008).
In this paper, we study the following Hamiltonian elliptic system with gradient term and inverse square potential
$ \left\{ \begin{array}{ll}-\Delta u +\vec{b}(x)\cdot \nabla u +V(x)u-\frac{\mu}{|x|^{2}}v=H_{v}(x,u,v)\\-\Delta v -\vec{b}(x)\cdot \nabla v +V(x)v-\frac{\mu}{|x|^{2}}u=H_{u}(x,u,v)\\\end{array} \right.$
for $x\in\mathbb{R}^{N}$, where $N\geq3$, $\mu\in\mathbb{R}$, and $V(x)$, $\vec{b}(x)$ and $H(x, u, v)$ are $1$-periodic in $x$. Under suitable conditions, we prove that the system possesses a ground state solution via variational methods for sufficiently small $\mu\geq0$. Moreover, we provide the comparison of the energy of ground state solutions for the case $\mu>0$ and $\mu=0$. Finally, we also give the convergence property of ground state solutions as $\mu\to0^+$.
Keywords: Hamiltonian elliptic systems, ground state solutions, inverse square potential, strongly indefinite functional.
Mathematics Subject Classification: 35J50, 58E05.
Citation: Jian Zhang, Wen Zhang, Xianhua Tang. Ground state solutions for Hamiltonian elliptic system with inverse square potential. Discrete & Continuous Dynamical Systems, 2017, 37 (8) : 4565-4583. doi: 10.3934/dcds.2017195
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