Abstract
In this paper, we study the following Hamiltonian elliptic system with gradient termfor , where , is a small positive parameter, is a constant vector, and . Suppose that has at least one maximum, we prove that the system has ground state solutions for all sufficiently small . Moreover, we show that these solutions converge to the ground state solutions of the associated limit problem and concentrate to the maxima of in certain sense as .
Notes
This work is partially supported by the Hunan Provincial Innovation Foundation For Postgraduate (No: CX2013A003) and the NNSF (No: 11171351, 11361078) and SRFDP (No: 20120162110021) of China.