PUBLICATIONS

Books

  1. Boundary Element Methods, Academic Press, London, March 1992. (with G. Chen)
  2. Vibration and Damping in Distributed Systems, Vol. I: Analysis, Estimation, Attenuation and Design, CRC Press, Boca Raton, Florida, 1993. (with G. Chen)
  3. Vibration and Damping in Distributed Systems, Vol. II: WKB and Wave Methods, Visualization and Experimentation, CRC Press, Boca Raton, Florida, 1993. (with G. Chen)
  4. Control of Nonlinear Distributed Parameter Systems, (pdf version)., Marcel Dekker, (edited with G. Chen and I. Laseicka)
  5. Boundary Element Methodsi with Applications to Nonlinear Problems, Atlantis Press, Ansterdam-Paris, 2010. (with G. Chen)

Research Papers

  1. "Partial Newton-correction method for multiple fixed points of semi-linear differential operators by Legendre-Gauss-Lobatto pseudospectral method"(pdf version),, J. Sci. Comp. To appear. (with Z.X. Li and F. Zhang)
  2. "Local min-orthogonal principle and its applications for solving multiple solution problems", EJDE Special Issue 02(2023), 175-192. (with M. Li and B. Ji)
  3. "An Improved Local-Min-Orthogonal Method for Finding Multiple Solutions to Nonlinear Elliptic PDEs",J. Sci. Comp. Published online May 16, 2022. (with X. Chen and Z. Li)
  4. "Solving a Singularly Perturbed Neumann Problem for Multiple Solutions"(pdf version),SIAM J. Sci. Comp. 44 (2022) 501-523. (with Y. Yuan and Z. Xie)
  5. "A new augmented singular transform and its partial Newton-correction method for finding more solutions to nonvariational quasilinear elliptic PDEs"(journal version), J. Comp. & Appl. Math, 376 (2020) 112821. (with Z. Li)
  6. "A New Augmented Singular Transform and its Partial Newton-Correction Method for Finding More Solutions" (pdf version), J. Sci. Comp., 71 (2017) 634-665. (with Z. Li and Z.Q. Wang)
  7. "Solving Multiple Solution Problems: Computational Methods and Theory Revisited" (pdf version),Communication on Applied Mathematics and Computation, 31 (2017) 1-31.
  8. "A Local Minimax Method Using Virtual Geometric Objects: Part I---For Finding Saddles"(pdf version), ,J. Sci. Comp., 78 (2019) 202-225. (with Z. Li and B.B. Ji)
  9. "A Local Minimax Method Using Virtual Geometric Objects: Part II---For Finding Equality Constrained Saddles"(pdf version), ,J. Sci. Comp., 78 (2019) 226-245 (with Z. Li)
  10. "Finding Gateaux-Saddles by a Local Minimax Method" ,NFAO, 38 (2017) 205-223. (with M. Li)
  11. "A Multiscale Enrichment Procedure for Nonlinear Monotone Operators" ,M2AN, 48 (2014) 475-491. (with Y. Efendiev, J. Galvis, M. Presho)
  12. "An Augmented Singular Transform and its Partial Newton Method for Finding Multiple Solutions" (pdf version),JCAM, 286(2015) 145-157. (with W. Yi, and Z. Xie)
  13. "A new approach for numerically solving nonlinear eigensolution problems"(pdf version),J. Sci. Comp., 64 (2015) 109-129. (with C. Wang)
  14. "Estimate of Morse Index of Cooperative Elliptic Systems and its Application to Spatial Vector Solitons" , J. Computat. Appl. Math.281(2015) 169-181. (with X. Chen)
  15. "An Orthogonal Subspace Minimization Method for Finding Multiple Solutions to Defocusing Schrodinger Equation with Symmetries"(pdf version),NMPDE, 29(2013) 1778-1800. (with C. Wang)
  16. "Global Sequence Convergence of a Local MiniMax Method for Finding Multiple Solutions in Banach Spaces" ,NFAO.32(2011) 1365-1380.
  17. "On Finding Multiple Solutions to a Singularly Perturbed Neumann Problem ",(pdf version) ,SIAM J. Sci. Comp., 34(2012) 395-420. (with Z.Q. Xie and Y.J. Yuan)
  18. "Finding Multiple Solutions to Elliptic PDE with Nonlinear Boundary Conditions ",(pdf version) ,J. Scientific Computing, 56(2013) 591-615. (with A. Le and Z.-Q. Wang)
  19. "A Local Min-Max-Orthogonal Method for Finding Multiple Solutions to Noncooperative Elliptic Systems",(pdf version) ,Math. Comp. 79(2010) 2213-2236. (with X. Chen)
  20. "A Local Min-Orthogonal Method for Multiple Solutions of Strongly Coupled Elliptic Systems",Discrete and Continuous Dynamical Systems, Supplement (2009) 151-160. (with X. Chen)
  21. ``Numerical Methods for Computing Nonlinear Eigenpairs. Part II. Non Iso-Homogenous Cases'', (pdf version), SIAM J. Sci. Comp. 30(2008) 937-956. (with X. Yao)
  22. ``On Homotopy Continuation Method for Computing Multiple Critical Points'', (pdf version) Numer. Methods Partial Differential Equations 24 (2008), no. 3, 728--748.(with X. Chen)
  23. ``A Numerical Method for Finding Multiple Co-existing Solutions to Nonlinear Cooperative Systems'', Applied Numerical Mathematics 58 (2008), pp. 1614-1627 (with X. Chen and X. Yao)
  24. ``Optimization with Some Uncontrollable Variables: A Min-Equilibrium Approach'', (pdf version) Journal of Industrial and Management Optimization (JIMO). 3 (2007), 129-138.
  25. ``Numerical Methods for Computing Nonlinear Eigenpairs. Part I. Iso-Homogenous Cases'', (pdf version), SIAM J. Sci. Comp., 29 (2007) 1355-1374. (with X. Yao)
  26. ``Unified Convergence Results on a Minimax Algorithm for Finding Multiple Critical Points in Banach Spaces'' (pdf version), SIAM J. Num. Anal., 45 (2007) 1330-1347. (with X. Yao)
  27. ``Numerical Methods for Computing Nonlinear Eigenpairs. Part III ---Using Partial Variation'', Preprint. (with X. Yao)
  28. ``Mathematical Analysis of a Bohr Atom Model'', J. Math. Physics, 47(2006), 022107, 23 pp. (with G. Chen, Z. Ding, S.-B. Hsu and M. Kim)
  29. ``A Numerical Based Investigation on the Symmetry Breaking and Asymptotic Behavior of the Ground States to the p-Henon Equation'', Electron. J. Diff. Equ. , 20(2011), 1-23. (with X. Yao)
  30. ``Saddle critical point analysis and computation'', (pdf version), Nonlinear Analysis, 63(2005) 1000-1009.
  31. ``The uniqueness of cross-validation selected smoothing parameters in kernel estimation'', Econometric Theory.(B), 21(2005), 1017-1025. (with Q. Li)
  32. ``A Local Minimax Characterization for Computing Multiple Nonsmooth Saddle Critical Points'', (pdf version), Math. Prog.(B), 104(2005), 749-760. (with X. Yao)
  33. ``Stabilization in computing saddle points''. Control and boundary analysis, 281--292, Lect. Notes Pure Appl. Math., 240, Chapman & Hall/CRC, Boca Raton, FL, 2005. (with X. Yao)
  34. ``A Local Minimax-Newton Method for Finding Critical Points with Symmetries'', (pdf version) SIAM J. Num. Anal., 42(2004), 1745-1759. (with Z.Q. Wang)
  35. ``A Minimax Method for Finding Multiple Critical Points in Banach Spaces and Its Application to Quasilinear Elliptic PDE'', (pdf version) SIAM J. Sci. Comp., 26(2005), 1796-1809. (with X. Yao)
  36. ``Chaotic vibration of the wave euqation with nonlinear feedback boundary control: progress and Open questions'', in Chaos Control (G.Chen and X.Yu, Eds.), LNCIS 292, pp. 25-50, Springer-Verlag Berlin Heidelberg, 2003. (with G. Chen and S. B. Hsu)
  37. ``Computational theory and methods for finding multiple critical points'', (pdf version), in `Topological Methods, Variational Methods and Their Applications', (H. Brezis, K.C. Chang, S.J. Li and P. Rabinowitz, Eds), World Scientific, New Jersey, 2003. pp.277-287.
  38. ``Convergence analysis of an optimal scaling algorithm for semilinear elliptic boundary value problems'', (pdf version), Contemporary Math. 357(2004), American Mathematical Society, pp. 69-84. (with G. Chen and B. G. Englert)
  39. ``A note on the elliptic Sine-Gordon equation'', (pdf version), Contemporary Math. 357(2004), American Mathematical Society, pp. 49-67. (with G. Chen, Z. Ding, C.R. Hu and W.M. Ni)
  40. ``Semilinear elliptic boundary value problems with nonlinear oblique boundary conditions, a boundary element monotone iteration approach'', Contemporary Math. 357(2004), American Mathematical Society, pp. 17-48. (with G. Chen, Y. Deng and W.M. Ni)
  41. ``An efficient and stable method for computing multiple saddle points with symmetries'' (pdf version), SIAM J. Num. Anal., 43(2005), 891-907. (with Z.Q. Wang)
  42. ``A local min-orthogonal method for finding multiple saddle points'', (pdf version), JMAA, 291(2004), 66-81.
  43. ``Instability analysis of saddle points by a local minimax method'', (pdf version), Math. Comp. , 74(2005), 1391-1411.
  44. ``Algorithms and visualization for solutions of nonlinear elliptic equations, Part II: Dirichlet, Neumann and Robin boundary conditions and problems in 3D'' Int. J. Bifurcation \& Chaos, 7(2001) 1781-1799. (with G. Chen, W.-M. Ni, A. Porronnet)
  45. ``Local characterization of saddle points and their Morse indices'', (pdf version). Control of Nonlinear Distributed Parameter Systems, Marcel Dekker. 233-252. (with Y. Li)
  46. ``Nonisotropic spatiotemporal chaotic vibration of the wave equation due to mixing energy transport and a van der Pol boundary condition'', Int. J. Bifurcation \& Chaos, 12(2002) no. 3, 535-559. (with G. Chen and S. B. Hsu)
  47. ``Chaotic vibration of the wave euqation by nonlinear feedback boundary condition'', in Control of Chaos and Bifurcation in Engineering, G.R. Chen, ed., Chapter 7, pp. 131-154, CRC Press, Boca Raton, FL., October, 1999, (with G. Chen and S. B. Hsu)
  48. ``Chaotic Vibrations of an Infinite Dimensional Harmonic Oscillator Due to a Self-Excitation Boundary Condition---Part III: Natural hysteresis memory effects'', Int. J. Bifurcation \& Chaos, 8(1998), 447-470 (with G. Chen and S. B. Hsu)
  49. ``Chaotic Vibrations of an Infinite Dimensional Harmonic Oscillator Due to a Self-Excitation Boundary Condition---Part II: Energy pumping, period doubling and homoclinic orbits'', Int. J. Bifurcation & Chaos, 8(1998), 423-445 (with G. Chen and S. B. Hsu)
  50. ``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'', J. Math Physics, 39(1998), 6459-6489 (with G. Chen and S. B. Hsu)
  51. ``Convergence results of a local minimax method for finding multiple critical points'', SIAM Sci. Comp., 24(2002), 865-885. (pdf version), (with Y. Li)
  52. ``A minimax method for finding multiple critical points and its applications to semilinear elliptic PDEs'', SIAM Sci. Comp., 23(2001), 840-865 (pdf version), (with Y. Li)
  53. ``Algorithms and visualization for solutions of nonlinear elliptic equation, Part I: Dirichlet Problem'', Int. J. Bifurcation & Chaos, (pdf version), 7(2000), 1565-1612. (with G. Chen and W.M. Ni)
  54. ``On the Structure of Majority Preferences'',Preprint (with Y. Li)
  55. ``Chaotic Vibrations of an Infinite Dimensional Harmonic Oscillator Due to a Self-Excitation Boundary Condition--- Part III: Natural hysteresis memory effects'', Int. J. Bifurcation and Chaos, Vol. 8(1998) (with G. Chen and S. B. Hsu)
  56. ``Chaotic Vibrations of an Infinite Dimensional Harmonic Oscillator Due to a Self-Excitation Boundary Condition---Part II: Energy pumping, period doubling and homoclinic orbits'', Int. J. Bifurcation and Chaos, Vol. 8 (1998) (with G. Chen and S. B. Hsu)
  57. ``Robust boundary control of the Stokes' fluids with boundary point observations'' (pdf version), Preprint, (with P. You)
  58. ``Asymptotic Equipartition of Energy by Nodal Points of an Eigenfunction'', J. Math. Physics, 38(1997), 5350-5360, (with G. Chen and S. Fulling)
  59. ``Nonlinear boundary control of heat conduction in nonsmooth domain withs with point observations, Part II: Numerical Computation and analysis'', Preprint (with P. You)
  60. ``Nonlinear boundary control of heat conduction in nonsmooth domain withs with point observations, Part I: Characterization of optimal control'', Preprint (with P. You)
  61. ``The heat equation with nonlinear boundary conditions in nonsmooth domains: A boundary integral equation approach'', , Preprint (with P. You)
  62. ``Boundary Element---Monotone Iteration Scheme for a Coupled Semilinear Elliptic System'', Math. Comp. 69(1999) 629--652. (G. Chen, Y. Deng and W.M. Ni)
  63. ``Linear Superposition of Chaotic and Orderly Vibrations on Two Serially Connected Strings with a van Pol Joint'', Int. J. Bifurcation and Chaos, 6(1996) 1509-1527. (with G. Chen and S. Hsu)
  64. ``Regulatory Control Analysis with Citizen Suit Provisions'', J. Environmental Economics and Managements, submitted July 1995. (with C. Chang, J. Mjeld, and T. Ozuna)
  65. ``Optimal Boundary Control of Stokes Fluids with Point Velocity Observations'' (pdf version), SIAM J. Cont. Opt., 36(1998) 981-1004. (with P. You and Z. Ding)
  66. ``Chaotic Vibrations of an Infinite Dimensional Harmonic Oscillator Due to a Self-Excitation Boundary Condition---Part I: A single oscillator'', AMS Transaction, 1998 (with G. Chen and S. Hsu)
  67. ``Constrained LQR Problems in Elliptic Distributed Control Systems with Point Observations---on Convergence Rates'', SIAM J. Control Opt., 35(1997), 1739-1754 (with P. You)
  68. ``Constrained LQR Problems in Elliptic Distributed Control Systems with Point Observations---Convegence Results'', Appl. Math. Optim., 36(1997) 173-201. (with Z. Ding)
  69. ``Boundary Element---Monotone Iteration Scheme for Semilinear Elliptic Partial Differential Equations'', Math. Comp., 65(1996) 943-982. (with Y. Deng, G. Chen, and W. Ni)
  70. ``Constrained LQR problems governed by the potential equation on Lipschitz domains with point observations'', J. Math. Pures Appl., 74 (1995), 317--344. (with Z. Ding)
  71. ``Constrained LQR problems in elliptic distributed control systems with pointwise observations'', SIAM J. Control Optim., 34(1996), 264-294. (with Z. Ding and L. Ji)
  72. ``On the existence of equilibrium for abstract economy'', J. Math. Anal. Appl., 193(1995),839--858.
  73. ``The equivalence between the wave propagation method and Bolotin's method in the asymptotic estimation of eigenfrequencies of a rectangular plate'', Wave Motion, 16(1992), 285-297. (with G. Chen amd M. Coleman)
  74. ``Visualization of special eigenmode shapes of a vibrating elliptical membrane'', SIAM Review, 36(1994), 453--469. (with G. Chen and P. Morris)
  75. ``On transfer topological conditions and their applications to some fundamental theorems in mathematics'', in review. (with G. Tian)
  76. ``Extension of the Zorn lemma to general nontransitive binary relations'', J. Optimization Theory and Applications, 80(1994), 337-351.
  77. ``Boundary element method for shape (domain) optimization of linear-quadratic elliptic boundary control problems'', in Boundary Control and Variation, J.P. Zolesio ed. Lecture Notes in pure and Applied Mathematics, Marcel Dekker, New York, 163(1994) 27-72. (with G. Chen and R. McLean)
  78. ``Quasi-variational inequalities without concavity'', J. Math. Anal. Appl., 171(1993), 289-299. (with G. Tian)
  79. ``Some boundary control problems and computations for the linear elasto-static Kirchhoff plate on an exterior domain'', in Boundary Control and Boundary Variation, J.P. Zolesio ed., Lecture Notes in Control and Information Sciences, Springer Verlag,Berlin, 178(1992) 80--114. (with G. Chen)
  80. ``Transfer method in characterizing the existence of maximal elements for binary relations on compact or noncompact sets'' SIAM J. Opt., 2(1992), 360-375. (with G. Tian)
  81. ``The transfer continuities, generalization of Weierstrass and maximum theorems: a full characterization approach'', J. Mathematical Economics, 24(1995) 281-303. (with G. Tian)
  82. ``The maximum theorem and the existence of equilibrium in abstract economies without lower semicontinuity'', J. Math. Anal. Appl., 166(1992), 351-364. (with G. Tian)
  83. ``Characterizations of the existence of equilibria in games with discontinuous and nonquasiconcave payoffs: Theory and applications'', Review of Economic Studies, 60(1993), 935-948. (with M. Baye and G. Tian)
  84. ``Analysis of vibration eigenfrequencies of a thin plate by Keller-Rubinow's wave method I: clamped boundary conditions with rectangle or circular geometry'', SIAM J. Appl. Math., 51(1991) 967-983. (with G. Chen and M. Coleman)
  85. ``The wave method for determining the asymptotic damping rates of eigenmodes (I):The wave equation on a rectangular or circular domain'', SIAM J. Control Opt., 29(1991), 656-677. (with G. Chen)
  86. ``Quasi-variational inequalities with non-compact sets'', J. Math. Anal. Appl., 160(1991), 583-595. (with G. Tian)
  87. ``The boundary element method for shape control of distributed parameter elastic systems'', in ``Mechanics and Control of Space Structures'', p.p.315-348, AIAA Progress in Aeronautics and Astronautics, J.L.Junkins ed., AIAA, Washington, D.C., 1990. (with G. Chen)
  88. ``The wave propagation method for the analysis of boundary stabilization in vibrating structures'', SIAM J. Appl. Math., 50(1990), 1254-1283. (with G.Chen)
  89. ``Modelling, analysis and testing of dissipative beam joints---experiments and d ata smoothing'', Math. Comp. Modelling, 11 (1988), 1011-1016. (with G.Chen, S.G. Krantz, D.L. Russell, C.E. Wayne and H.H.West)
  90. ``Minimizing the reflection of waves by surface impedance using boundary elements and global optimization'', Wave Motion, 10(1988), 239-255. (with G. Chen and T. Bridges)
  91. ``Diagonal convexity conditions for problems in convex analysis and quasi-variational inequalities'', J. Math. Anal. Appl., 132(1988), 213-22 5. (with G. Chen)
  92. ``Minimax methods for open-loop equilibria in N-person differential games, Part I, Linear quadratic games and constrained games'', Proc. the Royal Society of Edinburgh, 103A(1986), 15-34. (with G. Chen and Q. Zheng)
  93. ``Optimal design of microwave stepped impedance transformer'', J. Shanghai Univ. of Sci. & Tech., 4(1985), 36-42. (with Q.Zheng and H.Wang)