Ground state solutions for Hamiltonian elliptic system with sign-changing potential

• Main Authors: Wen Zhang, Xiaoliang Xie, Heilong Mi
• Format: Article
• Language: English
• Published: Texas State University 2017-07-01
• Series: Electronic Journal of Differential Equations
• Subjects: Hamiltonian elliptic system; superquadratic; sign-changing potential; generalized weak linking theorem
• Online Access: http://ejde.math.txstate.edu/Volumes/2017/164/abstr.html

This article concerns the Hamiltonian elliptic system $$\displaylines{ -\Delta u +V(x)u=H_{v}(x, u, v),\quad x\in \mathbb{R}^N, \cr -\Delta v +V(x)v=H_{u}(x, u, v),\quad x\in \mathbb{R}^N, \cr u(x)\to 0,\quad v(x)\to 0, \quad \text{as } |x|\to \infty, }$$ where $z=(u,v): \mathbb{R}^{N}\to\mathbb{R}\times\mathbb{R}$, $N\geq 3$ and the potential V(x) is allowed to be sign-changing. Under weak superquadratic assumptions for the nonlinearities, by applying the variant generalized weak linking theorem for strongly indefinite problem developed by Schechter and Zou, we obtain the existence of nontrivial and ground state solutions.