In this article, the authors investigate the existence problem for Hardy Henon type strongly indefinite elliptic systems. Existence results are obtained for such systems with superlinear subcritical nonlinearities.
The authors consider the semilinear SchrSdinger equation -△Au＋Vλ（x）u= Q（x）｜u｜γ-2u in R^N, where 1 〈 γ 〈 2＊ and γ≠ 2, Vλ= V^＋ -λV^-. Exploiting the relation between the Nehari manifold and fibrering maps, the existence of nontrivial solutions for the problem is discussed.
The authors prove the existence of nontrivial solutions for the SchrSdinger equation -△u ＋ V（x）u =λf（x, u） in R^N, where f is superlinear, subcritical and critical at infinity, respectively, V is periodic.
The present paper deals with the long-time behavior of a class of nonautonomous retarded semilinear parabolic differential equations. When the time delays are small enough and the spectral gap conditions hold, the inertial manifolds of the nonautonomous retard parabolic equations are constructed by using the Lyapunov-Perron method.
Li Xiang Zhu Jianmin Huang Jianhua (Dept. of Math, and System Sci., Sci, School, National University of Defense Technology, Changsha 410073)
