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

- "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) - "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) - "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) - "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) - "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) - "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) - "Solving Multiple Solution Problems: Computational Methods and Theory Revisited"
(pdf version),
**Communication on Applied Mathematics and Computation,**31 (2017) 1-31. - "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) - "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) - "Finding Gateaux-Saddles by a Local Minimax Method"
,
**NFAO,**38 (2017) 205-223. (with M. Li) - "A Multiscale Enrichment Procedure for Nonlinear Monotone Operators"
,
**M2AN**, 48 (2014) 475-491. (with Y. Efendiev, J. Galvis, M. Presho) - "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) - "A new approach for numerically solving nonlinear eigensolution problems"(pdf version),
**J. Sci. Comp.,**64 (2015) 109-129. (with C. Wang) - "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) - "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) - "Global Sequence Convergence of a Local MiniMax Method for Finding Multiple
Solutions in Banach Spaces"
,
**NFAO.**32(2011) 1365-1380. - "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) - "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) - "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) - "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) - ``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) - ``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) - ``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) - ``Optimization with Some Uncontrollable Variables: A Min-Equilibrium Approach'', (pdf version)
**Journal of Industrial and Management Optimization (JIMO).**3 (2007), 129-138. - ``Numerical Methods for Computing Nonlinear Eigenpairs. Part I.
Iso-Homogenous Cases'', (pdf version),
**SIAM J. Sci. Comp.**, 29 (2007) 1355-1374. (with X. Yao) - ``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) - ``Numerical Methods for Computing Nonlinear Eigenpairs. Part III
---Using Partial Variation'',
**Preprint.**(with X. Yao) - ``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) - ``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) - ``Saddle critical point analysis and computation'', (pdf version),
**Nonlinear Analysis**, 63(2005) 1000-1009. - ``The uniqueness of cross-validation selected smoothing parameters in
kernel estimation'',
**Econometric Theory.(B)**, 21(2005), 1017-1025. (with Q. Li) - ``A Local Minimax Characterization for Computing Multiple Nonsmooth Saddle
Critical Points'', (pdf version),
**Math. Prog.(B)**, 104(2005), 749-760. (with X. Yao) - ``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)
- ``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) - ``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) - ``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)
- ``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.
- ``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)
- ``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)
- ``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)
- ``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) - ``A local min-orthogonal method for finding multiple saddle points'',
(pdf version),
**JMAA**, 291(2004), 66-81. - ``Instability analysis of saddle points by a local minimax method'',
(pdf version),
**Math. Comp.**, 74(2005), 1391-1411. - ``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) - ``Local characterization of saddle points and their Morse indices'', (pdf version). Control of Nonlinear Distributed Parameter Systems, Marcel Dekker. 233-252. (with Y. Li)
- ``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) - ``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)
- ``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) - ``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) - ``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) - ``Convergence results of a local minimax method for finding
multiple critical points'',
**SIAM Sci. Comp.**, 24(2002), 865-885. (pdf version), (with Y. Li) - ``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) - ``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) - ``On the Structure of Majority Preferences'',Preprint (with Y. Li)
- ``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) - ``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) - ``Robust boundary control of the Stokes' fluids with boundary point observations'' (pdf version), Preprint, (with P. You)
- ``Asymptotic Equipartition of Energy by Nodal Points of an Eigenfunction'',
**J. Math. Physics**, 38(1997), 5350-5360, (with G. Chen and S. Fulling) - ``Nonlinear boundary control of heat conduction in nonsmooth domain withs with point observations, Part II: Numerical Computation and analysis'', Preprint (with P. You)
- ``Nonlinear boundary control of heat conduction in nonsmooth domain withs with point observations, Part I: Characterization of optimal control'', Preprint (with P. You)
- ``The heat equation with nonlinear boundary conditions in nonsmooth domains: A boundary integral equation approach'', , Preprint (with P. You)
- ``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) - ``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) - ``Regulatory Control Analysis with Citizen Suit Provisions'',
**J. Environmental Economics and Managements**, submitted July 1995. (with C. Chang, J. Mjeld, and T. Ozuna) - ``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) - ``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) - ``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) - ``Constrained LQR Problems in Elliptic
Distributed Control Systems with Point Observations---Convegence Results'',
**Appl. Math. Optim.**, 36(1997) 173-201. (with Z. Ding) - ``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) - ``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) - ``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) - ``On the existence of equilibrium for abstract economy'',
**J. Math. Anal. Appl.**, 193(1995),839--858. - ``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) - ``Visualization of special eigenmode shapes of a vibrating elliptical
membrane'',
**SIAM Review**, 36(1994), 453--469. (with G. Chen and P. Morris) - ``On transfer topological conditions and their applications to some fundamental theorems in mathematics'', in review. (with G. Tian)
- ``Extension of the Zorn lemma to general nontransitive binary
relations'',
**J. Optimization Theory and Applications**, 80(1994), 337-351. - ``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)
- ``Quasi-variational inequalities without
concavity'',
**J. Math. Anal. Appl.**, 171(1993), 289-299. (with G. Tian) - ``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)
- ``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) - ``The transfer continuities, generalization of
Weierstrass and maximum theorems: a full characterization approach'',
**J. Mathematical Economics**, 24(1995) 281-303. (with G. Tian) - ``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) - ``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) - ``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) - ``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) - ``Quasi-variational inequalities with non-compact
sets'',
**J. Math. Anal. Appl.**, 160(1991), 583-595. (with G. Tian) - ``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)
- ``The wave propagation method for the analysis of boundary stabilization
in vibrating structures'',
**SIAM J. Appl. Math.**, 50(1990), 1254-1283. (with G.Chen) - ``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) - ``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) - ``Diagonal convexity conditions for problems in convex analysis and
quasi-variational inequalities'',
**J. Math. Anal. Appl.**, 132(1988), 213-22 5. (with G. Chen) - ``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) - ``Optimal design of microwave stepped impedance transformer'',
**J. Shanghai Univ. of Sci. & Tech.**, 4(1985), 36-42. (with Q.Zheng and H.Wang)