Ground state solutions for Hamiltonian elliptic systems with super or asymptotically quadratic nonlinearity
Ground state solutions for Hamiltonian elliptic systems with super or asymptotically quadratic nonlinearity
Abstract This article concerns the Hamiltonian elliptic system: $$ \textstyle\begin{cases} -\Delta \varphi +V(x)\varphi =G_{\psi }(x,\varphi ,\psi ) & \mbox{in } \mathbb {R}^{N}, \\ -\Delta \psi +V(x)\psi =G_{\varphi }(x,\varphi ,\psi ) & \mbox{in } \mathbb {R}^{N}, \\ \varphi , \psi \in H^{1}(\mathbb {R}^{N}). \end{cases} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>{</mml:mo> <mml:mtable> <mml:mtr> …