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Solutions for a class of nonperiodic superquadratic Hamiltonian elliptic systems involving gradient terms. (English) Zbl 1375.35154

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.

MSC:

35J47 Second-order elliptic systems
35J50 Variational methods for elliptic systems
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