In this paper,we study the ground state solution to the Dirac equation-i∑3k=1αk∂ku+aβu+M(x)u=g(x,|u|)u,where the potential function M(x)is periodic when the nonlinear function g satisfies the super-quadratic and local super-quadratic growth conditions at infinity respectively.The existence of Nehari-Pankov-type ground states is proved using the non-Nehari manifold method without strictly monotone conditions.We primarily overcome two major difficulties:(1)the strongly indefinite associated functional,i.e.,the workspace is decomposed into positive and negative subspaces,both with infinite dimensions,which makes the classical critical point theorem unable to be directly applied;(2)verification of the link geometry and the boundedness of Cerami sequences when the nonlinearity is not globally super-quadratic at infinity.
关键词
基态解/Dirac方程/非Nehari流形方法
Key words
ground state solution/Dirac equation/non-Nehari manifold method
维普
万方数据