Solutions for a class of nonperiodic superquadratic Hamiltonian elliptic systems involving gradient terms (Q2398769)

Summary: In the present paper, we consider the following Hamiltonian elliptic system (HES): \(- \Delta u + b \left(x\right) \cdot \nabla u + V \left(x\right) u = H_v \left(x, u, v\right)\), \(x \in \mathbb{R}^N\), \(- \Delta v - b \left(x\right) \cdot \nabla v + V \left(x\right) v = H_u \left(x, u, v\right)\), \(x \in \mathbb{R}^N \). A new existence result of nontrivial solutions is obtained for the system (HES) via variational methods for strongly indefinite problems, which generalizes some known results in the literatures.