selected publications academic article Li, Z., Wang, Z., & Zhou, J. (2016). A New Augmented Singular Transform and its Partial Newton-Correction Method for Finding More Solutions. Journal of Scientific Computing. 71(2), 634-659. Li, M., & Zhou, J. (2016). Finding Gateaux-Saddles by a Local Minimax Method. Numerical Functional Analysis and Optimization. 38(2), 205-223. Xie, Z., Yi, W., & Zhou, J. (2015). An augmented singular transform and its partial Newton method for finding new solutions. Journal of Computational and Applied Mathematics. 286, 145-157. Chen, X., & Zhou, J. (2015). Estimate of Morse index of cooperative elliptic systems and its application to spatial vector solitons. Journal of Computational and Applied Mathematics. 281, 169-181. Efendiev, Y., Galvis, J., Presho, M., & Zhou, J. (2014). A Multiscale Enrichment Procedure for Nonlinear Monotone Operators. ESAIM Mathematical Modelling and Numerical Analysis. 48(2), 475-491. Wang, C., & Zhou, J. (2014). A New Approach for Numerically Solving Nonlinear Eigensolution Problems. Journal of Scientific Computing. 64(1), 109-129. Wang, C., & Zhou, J. (2013). An orthogonal subspace minimization method for finding multiple solutions to the defocusing nonlinear Schrödinger equation with symmetry. Numerical Methods for Partial Differential Equations. 29(5), 1778-1800. Le, A. n., Wang, Z., & Zhou, J. (2013). Finding Multiple Solutions to Elliptic PDE with Nonlinear Boundary Conditions. Journal of Scientific Computing. 56(3), 591-615. Xie, Z., Yuan, Y., & Zhou, J. (2012). On Finding Multiple Solutions to a Singularly Perturbed Neumann Problem. SIAM JOURNAL ON SCIENTIFIC COMPUTING. 34(1), a395-a420. Yao, X., & Zhou, J. (2011). A numerically based investigation on the symmetry breaking and asymptotic behavior of the ground states to the p-Hénon equation. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS. 2011. Zhou, J. (2011). Global Sequence Convergence of a Local Minimax Method for Finding Multiple Solutions in Banach Spaces. Numerical Functional Analysis and Optimization. 32(12), 1365-1380. Chen, X., & Zhou, J. (2010). A local min-max-orthogonal method for finding multiple solutions to noncooperative elliptic systems. MATHEMATICS OF COMPUTATION. 79(272), 2213-2236. Chen, X., Zhou, J., & Yao, X. (2008). A numerical method for finding multiple co-existing solutions to nonlinear cooperative systems. Applied Numerical Mathematics. 58(11), 1614-1627. Chen, X., & Zhou, J. (2008). On homotopy continuation method for computing multiple solutions to the Henon equation. Numerical Methods for Partial Differential Equations. 24(3), 728-748. Yao, X., & Zhou, J. (2008). Numerical Methods for Computing Nonlinear Eigenpairs: Part II. Non-Iso-Homogeneous Cases. SIAM JOURNAL ON SCIENTIFIC COMPUTING. 30(2), 937-956. Yao, X., & Zhou, J. (2007). Numerical Methods for Computing Nonlinear Eigenpairs: Part I. Iso-Homogeneous Cases. SIAM JOURNAL ON SCIENTIFIC COMPUTING. 29(4), 1355-1374. Zhou, J. (2007). Optimization with some uncontrollable variables: a min-equilibrium approach. Journal of Industrial & Management Optimization. 3(1), 129-138. Yao, X., & Zhou, J. (2007). Unified Convergence Results on a Minimax Algorithm for Finding Multiple Critical Points in Banach Spaces. SIAM Journal on Numerical Analysis. 45(3), 1330-1347. Chen, G., Ding, Z., Hsu, S., Kim, M., & Zhou, J. (2006). Mathematical analysis of a Bohr atom model. Journal of Mathematical Physics. 47(2), 022107-022107. Zhou, J. (2005). Saddle critical point analysis and computation. Nonlinear Analysis. 63(5-7), 1000-1009. Li, Q. i., & Zhou, J. (2005). THE UNIQUENESS OF CROSS-VALIDATION SELECTED SMOOTHING PARAMETERS IN KERNEL ESTIMATION OF NONPARAMETRIC MODELS. ECONOMETRIC THEORY. 21(5), 1017-1025. Yao, X., & Zhou, J. (2005). A local minimax characterization for computing multiple nonsmooth saddle critical points. Mathematical Programming. 104(2-3), 749-760. Yao, X., & Zhou, J. (2005). A Minimax Method for Finding Multiple Critical Points in Banach Spaces and Its Application to Quasi-linear Elliptic PDE. SIAM JOURNAL ON SCIENTIFIC COMPUTING. 26(5), 1796-1809. Zhou, J. (2004). Instability analysis of saddle points by a local minimax method. MATHEMATICS OF COMPUTATION. 74(251), 1391-1411. Zhou, J. (2004). A local min-orthogonal method for finding multiple saddle points. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. 291(1), 66-81. Wang, Z., & Zhou, J. (2004). A Local Minimax-Newton Method for Finding Multiple Saddle Points with Symmetries. SIAM Journal on Numerical Analysis. 42(4), 1745-1759. Li, Y., & Zhou, J. (2003). Convergence Results of a Local Minimax Method for Finding Multiple Critical Points. SIAM JOURNAL ON SCIENTIFIC COMPUTING. 24(3), 865-885. CHEN, G., HSU, S., & ZHOU, J. (2002). NONISOTROPIC SPATIOTEMPORAL CHAOTIC VIBRATION OF THE WAVE EQUATION DUE TO MIXING ENERGY TRANSPORT AND A VAN DER POL BOUNDARY CONDITION. International Journal of Bifurcation and Chaos. 12(03), 535-559. CHEN, G., NI, W., PERRONNET, A., & ZHOU, J. (2001). ALGORITHMS AND VISUALIZATION FOR SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS, PART II: DIRICHLET, NEUMANN AND ROBIN BOUNDARY CONDITIONS AND PROBLEMS IN 3D. International Journal of Bifurcation and Chaos. 11(07), 1781-1799. Li, Y., & Zhou, J. (2001). A Minimax Method for Finding Multiple Critical Points and Its Applications to Semilinear PDEs. SIAM JOURNAL ON SCIENTIFIC COMPUTING. 23(3), 840-865. CHEN, G., ZHOU, J., & NI, W. (2000). ALGORITHMS AND VISUALIZATION FOR SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS. International Journal of Bifurcation and Chaos. 10(07), 1565-1612. Chen, G., Deng, Y. H., Ni, W. M., & Zhou, J. X. (2000). Boundary element monotone iteration scheme for semilinear elliptic partial differential equations, part II: Quasimonotone iteration for coupled 2 x 2 systems. MATHEMATICS OF COMPUTATION. 69(230), 629-652. Chen, G., Hsu, S., & Zhou, J. (1998). Snapback repellers as a cause of chaotic vibration of the wave equation with a van der Pol boundary condition and energy injection at the middle of the span. Journal of Mathematical Physics. 39(12), 6459-6489. You, P., Ding, Z., & Zhou, J. (1998). Optimal Boundary Control of the Stokes Fluids with Point Velocity Observations. SIAM Journal on Control and Optimization. 36(3), 981-1004. Chen, G., Hsu, S., & Zhou, J. (1998). Chaotic Vibrations of the One-Dimensional Wave Equation Due to a Self-Excitation Boundary Condition. International Journal of Bifurcation and Chaos. 08(03), 423-445. Chen, G., Hsu, S., & Zhou, J. (1998). Chaotic Vibrations of the One-Dimensional Wave Equation due to a Self-Excitation Boundary Condition. International Journal of Bifurcation and Chaos. 08(03), 447-470. Chen, G., Hsu, S., Zhou, J., Chen, G., & Crosta, G. (1998). Chaotic vibrations of the one-dimensional wave equation due to a self-excitation boundary condition. Part I: Controlled hysteresis. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. 350(11), 4265-4311. You, P., & Zhou, J. (1997). Constrained LQR Problems in Elliptic Distributed Control Systems with Point Observations--- on Convergence Rates. SIAM Journal on Control and Optimization. 35(5), 1739-1754. Ding, Z., & Zhou, J. (1997). Constrained LQR problems in elliptic distributed control systems with point observations—convergence results. Applied Mathematics & Optimization. 36(2), 173-201. CHEN, G., ZHOU, J., & HSU, S. (1996). LINEAR SUPERPOSITION OF CHAOTIC AND ORDERLY VIBRATIONS ON TWO SERIALLY CONNECTED STRINGS WITH A VAN DER POL JOINT. International Journal of Bifurcation and Chaos. 06(08), 1509-1527. Deng, Y., Chen, G., Ni, W., & Zhou, J. (1996). Boundary element monotone iteration scheme for semilinear elliptic partial differential equations. MATHEMATICS OF COMPUTATION. 65(215), 943-982. Ding, Z., Ji, L., & Zhou, J. (1996). Constrained LQR Problems in Elliptic Distributed Control Systems with Point Observations. SIAM Journal on Control and Optimization. 34(1), 264-294. Zhou, J. X. (1995). On the Existence of Equilibrium for Abstract Economies. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. 193(3), 839-858. Tian, G., & Zhou, J. (1995). Transfer continuities, generalizations of the Weierstrass and maximum theorems: A full characterization. Journal of Mathematical Economics. 24(3), 281-303. Chen, G., Morris, P. J., & Zhou, J. (1994). Visualization of Special Eigenmode Shapes of a Vibrating Elliptical Membrane. SIAM Review. 36(3), 453-469. Zhou, J. X. (1994). Extension of the Zorn lemma to general nontransitive binary relations. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. 80(2), 333-347. Baye, M. R., Tian, G., & Zhou, J. (1993). Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs. The Review of Economic Studies. 60(4), 935-948. Tian, G. Q., & Zhou, J. X. (1993). Quasi-Variational Inequalities without the Concavity Assumption. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. 172(1), 289-299. Tian, G., & Zhou, J. (1992). The maximum Theorem and the existence of Nash equilibrium of (generalized) games without lower semicontinuities. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. 166(2), 351-364. Tian, G., & Zhou, J. (1991). Quasi-variational inequalities with non-compact sets. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. 160(2), 583-595. Chen, G., Coleman, M. P., & Zhou, J. (1991). Analysis of Vibration Eigenfrequencies of a Thin Plate by the Keller-Rubinow Wave Method I: Clamped Boundary Conditions with Rectangular or Circular Geometry. SIAM Journal on Applied Mathematics. 51(4), 967-983. Zhou, J., & Chen, G. (1991). The Wave Method for Determining the Asymptotic Damping Rates of Eigenmodes I: The Wave Equation on a Rectangular or Circular Domain. SIAM Journal on Control and Optimization. 29(3), 656-677. Chen, G., & Zhou, J. (1990). The Wave Propagation Method for the Analysis of Boundary Stabilization in Vibrating Structures. SIAM Journal on Applied Mathematics. 50(5), 1254-1283. Chen, G., Bridges, T. J., & Zhou, J. (1988). Minimizing the reflection of waves by surface impedance using boundary elements and global optimization. Wave Motion. 10(3), 239-255. Zhou, J. X., & Chen, G. (1988). Diagonal convexity conditions for problems in convex analysis and quasi-variational inequalities. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. 132(1), 213-225. Chen, G., Krantz, S. G., Russell, D. L., Wayne, C. E., West, H. H., & Zhou, J. (1988). Modelling, analysis and testing of dissipative beam joints -experiments and data smoothing. Mathematical and Computer Modelling. 11(C), 1011-1016. Chen, G., Zheng, Q., & Zhou, J. (1986). Minimax methods for open-loop equilibria in N-person differential games. Part I: Linear quadratic games and constrained games*. Proceedings of the Royal Society of Edinburgh Section A Mathematics. 103(1-2), 15-34. book Chen, G., & Zhou, J. (2010). BOUNDARY ELEMENT METHODS WITH APPLICATIONS TO NONLINEAR PROBLEMS 2nd edition. Springer Science & Business Media. Chen, G., Lasiecka, I., & Zhou, J. (2001). Control Of Nonlinear Distributed Parameter Systems. Ed. Chen, Goong. CRC Press. Chen, G., & Zhou, J. (1993). Vibration and Damping in Distributed Systems Vol. I: Analysis, Estimation, Attenuation and Design. CRC Press. Chen, G., & Zhou, J. (1993). Vibration and Damping in Distributed Systems, Volume II: WKB and Wave Methods, Visualization and Experimentation. CRC Press. Chen, G., & Zhou, J. (1992). Boundary element methods. Academic Press. chapter Chen, G., Hsu, S., & Zhou, J. (2004). Chaotic Vibration of the Wave Equation with Nonlinear Feedback Boundary Control: Progress and Open Questions. ADVANCES IN COOPERATIVE CONTROL AND OPTIMIZATION. Chen, G., & Yu, X. (Eds.), Chaos Control. (pp. 25-50). Springer Berlin Heidelberg. conference paper Chen, G., & Zhou, J. (1990). Boundary element method for shape control of distributed parameter elastostatic systems. 161-175. Ji, L., & Zhou, J. (1990). The boundary element method for boundary control of the linear Stokes flow. 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601). 1192-1194. Zhou, J. (1989). Computations of eigenfunctions and eigenfrequencies of two dimensional vibrating structures by the boundary element method. 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601). 2045-2049. Chen, G., & Zhou, J. (1987). COMPUTING OPTIMAL BOUNDARY CONTROLS OF A PLATE BY THE BOUNDARY ELEMENT METHOD. 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601). 992-996.
teaching activities MATH308 Differential Equations Instructor MATH311 Top In Applied Math I Instructor MATH491 Hnr-research Instructor MATH602 Meth Appl Part Diff Eq Instructor MATH651 Optimization I Instructor MATH652 Optimization Ii Instructor MATH684 Professional Internship: In-ab Instructor MATH685 Directed Studies Instructor MATH691 Research Instructor MATH691 Research Instructor
chaired theses and dissertations Chen, Xianjin (2008-08). Analysis and computation of multiple unstable solutions to nonlinear elliptic systems. Wang, Changchun (2012-05). On Computing Multiple Solutions of Nonlinear PDEs Without Variational Structure. Yao, Xudong (2004-08). Minimax methods for finding multiple saddle critical points in Banach spaces and their applications.
education and training Ph.D. in Mathematics, Pennsylvania State University - (State College, Pennsylvania, United States) 1986