Acta mathematica scientia,Series B ›› 2018, Vol. 38 ›› Issue (6): 1966-1980.

• Articles • Previous Articles    

EXISTENCE OF GROUND STATE SOLUTIONS TO HAMILTONIAN ELLIPTIC SYSTEM WITH POTENTIALS

Wenbo WANG1,2, Quanqing LI3   

  1. 1 Wuhan Institute of Physics and Mathematics, CAS, Wuhan 430071, China;
    2 University of Chinese Academy of Sciences, Beijing 100049, China;
    3 Department of Mathematics, Honghe University, Mengzi 661100, China
  • Received:2017-03-06 Revised:2018-05-18 Online:2018-12-25 Published:2018-12-28
  • Supported by:
    This work was partially supported by the Honghe University Doctoral Research Program (XJ17B11) and Yunnan Province Applied Basic Research for Youths and the Yunnan Province Local University (Part) Basic Research Joint Project (2017FH001-013).

Abstract: In this paper, we investigate nonlinear Hamiltonian elliptic system

where N ≥ 3, τ > 0 is a positive parameter and V, K are nonnegative continuous functions, f and g are both superlinear at 0 with a quasicritical growth at infinity. By establishing a variational setting, the existence of ground state solutions is obtained.

Key words: Hamiltonian elliptic system, strongly indefinite functional, generalized Nehari manifold

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