American Journal of Mathematics and Statistics

American Journal of Mathematics and Statistics is to publish well-written original research articles and studies describing the latest research and developments in the field of mathematics and statistics. This is a broad-based journal covering all branches of mathematics, statistics and interdisciplinary research.

## Xiangjin XU

Editorial Board Member of American Journal of Mathematics and Statistics

Assistant Professor, Binghamton University-SUNY, USA

Research Areas

Harmonic Analysis on Manifolds and Nonlinear Differential Equations

### Education

 2004 PhD Mathematics, Johns Hopkins University 1999 M.S. Mathematics, Chern Institute of Mathematics 1996 B.S. Mathematics, Nankai University

### Experience

 2008 Centre de Recherches Mathematiques, Universite de Montreal, Postdoctoral Fellow 2007-current Department of Mathematical Sciences, Binghamton University-SUNY, Assistant Professor 2005 Mathematical Sciences Research Institute in Berkeley, Postdoctoral Fellow 2004-2007 Department of Mathematics, University of Virginia, Whyburn Instructor

### Publications: Conferences/Workshops/Symposiums/Journals/Books

 [1] Xiangjin Xu, Subharmonic solutions of a class of non-autonomous Hamiltonian systems. Acta Sci. Nat. Univer. Nankai. Vol. 32, No.2, (1999), pp. 46-50. [2] Yiming Long, Xiangjin Xu, Periodic solutions for a class of nonautonomous Hamiltonian systems. Nonlinear Anal. Ser. A: Theory Methods, 41 (2000), no. 3-4, 455-463. [3] Xiangjin Xu, Homoclinic orbits for first order Hamiltonian systems possessing super-quadratic potentials. Nonlinear Anal. Ser. A: Theory Methods, 51 (2002), no. 2, 197-214. [4] Xiangjin Xu, Periodic solutions for non-autonomous Hamiltonian systems possessing super-quadratic potentials. Nonlinear Anal. Ser. A: Theory Methods, 51 (2002), no. 6, 941-955. [5] Xiangjin Xu, Subharmonics for first order convex nonautonomous Hamiltonian systems. J. Dynam. Differential Equations 15 (2003), no. 1, 107-123. [6] Xiangjin Xu, Multiple solutions of super-quadratic second order dynamical systems. Discrete Contin. Dyn. Syst. 2003, suppl., 926-934. [7] Xiangjin Xu, Sub-harmonics of first order Hamiltonian systems and their asymptotic behaviors. Discrete Contin. Dyn. Syst. Ser. B 3 (2003), no. 4, 643-654. [8] Xiangjin Xu, Homoclinic orbits for first order Hamiltonian systems with convex potentials. Advanced Nonlinear Studies 6 (2006), 399-410. [9] Xiangjin Xu, New Proof of H\"ormander Multiplier Theorem on Compact manifolds without boundary. Proc. Amer. Math. Soc. 135 (2007), 1585-1595. [10] Roberto Triggiani, Xiangjin Xu, Pointwise Carleman Estimates, Global Uniqueness, Observability, and Stabilization for Schr\"odinger Equations on Riemannian Manifolds at the $H^1$-Level. AMS Contemporary Mathematics, Volume 426, 2007, 339-404. [11] Xiangjin Xu, Gradient estimates for eigenfunctions of compact manifolds with boundary and the H\"ormander multiplier theorem. Forum Mathematicum 21:3 (May 2009), pp. 455-476. [12] Xiangjin Xu, Eigenfunction estimates for Neumann Laplacian on compact manifolds with boundary and multiplier problems. Proc. Amer. Math. Soc. 139 (2011), 3583-3599. [13] Junfang Li, Xiangjin Xu, Differential Harnack inequalities on Riemannian manifolds I : linear heat equation.Advance in Mathematics, Volume 226, Issue 5, (March, 2011) Pages 4456-4491 doi:10.1016/j.aim.2010.12.009 [14] Liangui Wang, Xiangjin Xu, Hybrid state feedback, robust $H_{\infty}$ control for a class switched systems with nonlinear uncertainty. (Accepted by conference proceeding of CSIE2011 , to be published in the Springer Lecture Notes in Electrical Engineering (LNEE)) [15] Xiangjin Xu, Gradient estimates for $u_t=\Delta F(u)$ on manifolds and some Liouville-type theorems. Journal of Differential Equation (2011) doi:10.1016/j.jde.2011.08.004 [16] Xiangjin Xu, Upper and lower bounds for normal derivatives of spectral clusters of Dirichlet Laplacian. Journal of Mathematical Analysis and Applications (2011) doi:10.1016/j.jmaa.2011.09.003