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Applicable Analysis
An International Journal
Volume 94, 2015 - Issue 7
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Articles

On semiclassical ground state solutions for Hamiltonian elliptic systems

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Pages 1380-1396 | Received 05 Nov 2013, Accepted 03 Jun 2014, Published online: 04 Jul 2014
 

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 .

AMS Subject Classifications:

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.

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