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

Duan, Shengzhong; Wu, Xian

Discrete Dyn. Nat. Soc. 2017, Article ID 9125486, 15 p. (2017).

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

Keywords:

Hamiltonian elliptic system; variational methods

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