On semiclassical ground state solutions for Hamiltonian elliptic systems

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 .

Keywords:

• Hamiltonian elliptic systems
• semiclassical ground states
• concentration
• strongly indefinite functionals

AMS Subject Classifications:

• 35J50
• 58E05

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.