Zhi-Qiang Wang

Professor of Pure and Applied Mathematics

Dr. Wang graduated in 1982 from Jilin University China majoring in mathematics, and received his MS degree and PhD degree in mathematics from the Chinese Academy of Sciences, in 1984 and 1986, respectively. After post-doctoral training in Peking University and Courant Institute of New York University, and holding visiting positions at University of Utah and University of Wisconsin, he joined Utah State University in 1991 as an assistant professor. He was promoted to associated professor with tenure in 1994 and to full professor in 1998. He served from 1994-1997 as Director of Graduate Studies in Mathematics and Statistics at Utah State University. In 1998 he was awarded Researcher of The Year in the College of Sciences at Utah State University. He was elected a Fellow of American Mathematical Society in 2014.

Research Interests

Nonlinear Partial Differential Equations
Variational and Topological Methods in Nonlinear Analysis
Hamiltonian Systems
Numerical Algorithms

Some Publications (complete listing from MathSciNet ) (citations from AMS citation database ) (Google Scholar )

On a superlinear elliptic equation , Annales de l'Institut Henri Poincar$\acute{e}$ - Analyse non lin$\acute{e}$aire , { 8}(1991), 43-57.
On the existence of multiple, single-peaked solutions of a semilinear Neumann problem , Archive for Rational Mechanics and Analysis , { 120}(1992), 375-399.
Existence and multiplicity results for some superlinear elliptic problems on $R^N$ , (with T. Bartsch) Communications in Partial Differential Equations , {20} (1995), 1725 -1741.
On the existence of sign changing solutions for semilinear Dirichlet problems , (with T. Bartsch) Topological Methods in Nonlinear Analysis , { 7} (1996), 115 - 131.
Periodic solutions of even Hamiltonian systems on the torus (1997) , (with Thomas Bartsch) Mathematische Zeitschrift , 224, 65-76.
Periodic solutions of even, spatially periodic Hamiltonian systems (1997) , (with Thomas Bartsch) Journal of Differential Equations , 135, 103-128.
On Neumann problems for semilinear elliptic equations with critical nonlinearity: existence and symmetry of multi-peaked solutions (1997) , (with Stani Maier and Klaus Schmitt) Communications in Partial Differential Equations , 22, 1493 - 1527.
Even Hamiltonian systems on tori and cotangent spaces of tori (1997) , (with Thomas Bartsch) Nonlinear Analysis, Theory, Methods and Applications , 30, 4123 - 4134.
Existence, nonexistence and symmetry property of local and global minimizers for a semilinear elliptic problem (1998) , Discrete and Continuous Dynamical Systems , Special Vol. 2, 288 - 302.
Multiplicity for symmetric indefinite functionlas: applications to Hamiltonian and elliptic systems (1998) , (with Patricio Felmer) Topological Methods in Nonlinear Analysis , 12, 207 - 226.
Existence and nonexistence of $G$-least energy solutions for a nonlinear Neumann problem (1999) , Calculus of Variations and Partial Differential Equations , 8, 109 - 122.
Existence of many positive solutions of an elliptic equation with critical exponent on an annulus (1999) , (with Michel Willem) Proccedings of American Mathematical Society , 127, 1711 - 1714.
Nonlinear elliptic equations on expaning symmetric domains (1999) , (with Florin Catrina) Journal of Differential Equations , 156, 153 - 181.
Existence and symmetry of multi-bump solutions for nonlinear Schr\"odinger equations (1999) , Journal of Differential Equations , 159, 102 - 137.
Positive solutions for elliptic equations with critical growth in unbounded domains , (with M. Ramos and M. Willem) Calculus of variations and differential equations (Haifa, 1998) , 192 - 199, Chapman \& Hall/CRC Res. Notes Math., 410, Chapman \& Hall/CRC, Boca Raton, FL, 2000.
Mountain Pass Theorem in Order Intervals and Multiple Solutions for Semilinear Elliptic Dirichlet Problems (2000) , (with S. Li) Journal d'Analyse Math\'ematiques , 81, 373-396.
Singular minimization problems (2000) , (with M. Willem) Journal of Differential Equations , 161, 307 - 320.
Morse theory without (PS) condition at isolated values and strong resonant problems (2000) , (with N. Hirano and S. Li) Calculus of Variations and Partial Differential Equations , 10, 223 - 247.
On the Morse indices of sign-changing solutions for nonlinear elliptic problems (2000) , (with T. Bartsch and K.C. Chang) Mathematische Zeitschrift , 233, 366-384.
Multiple positive solutions for a nonlinear Schr\"odinger equation (2000) , (with T. Bartsch) Zeitschrift f\"{u}r Angewandte Mathematik und Physik , 51, 366-384.
Symmetric solutions for the prescribed scalar curvature problem (2000) , (with F. Catrina) Indinna University Mathematical Journal , 49, 779-813.
On the Caffarelli-Kohn -Nirenberg Inequalities (2000) , (with F. Catrina) Comptes Rendus des S\'eances de l'Acad\'emie des Sciences. S\'erie I. Math\'ematique , 330, 437 - 442.
On the Caffarelli-Kohn -Nirenberg Inequalities (2000) , (with F. Catrina) Comptes Rendus des S\'eances de l'Acad\'emie des Sciences. S\'erie I. Math\'ematique , 330, 437 - 442.
On the Caffarelli-Kohn-Nirenberg Inequalities: sharp constants, existence (and nonexistence) and symmetry of extremal functions , (with F. Catrina) Communications on Pure and Applied Mathematics , Vol. LIV (2001), 229-258.
Asymptotic uniqueness and exact symmetry of k-bump solutions for a class of degenerate elliptic problems , (with F. Catrina) DCCD, , Add. Vol. III (2001), 80-88.
Positive bound states having prescribed symmetry for a class of nonlinear elliptic equations in $R^N$ , (with F. Catrina) Annales de l'Institut Henri Poincare - Analyse non lineaire , 18 (2001), 157-178.
Gluing approximate solutions of minimum type on the Nehari manifold , (with Yanyan Li) USA-Chile Workshop on Nonlinear Analysis , in press.
Nonlinear Schr\"odinger equations with steep potential well , (with Thomas Bartsch and Alexander Pankov) Communications in Contemporary Mathematics , 3 (2001), 1 - 21.
On the existence of soliton solutions to quasilinear Schr\"odinger equations , (with M. Poppenburg and K. Schmitt) Calculus of Variations and Partial Differential Equations, , 14 (2002) 3, 329-344.
Symmetry Breaking of Extremal Functions for the Caffarelli-Kohn-Nirenberg Inequalities , (with J. Byeon) Communications in Contemporary Mathematics , 4 (2002), 457-466.
Lusternik-Schnirelman theory in partially ordered Hilbert spaces , (with S. J. Li) Transactions of American Mathematical Society , 354 (2002), 3207-3227.
Soliton Solutions for Quasilinear Schr\"odinger Equations , (with J. Liu) Proceedings of the American Mathematical Society , 131 (2003), 441-448.
Soliton Solutions for Quasilinear Schr\"odinger Equations, II , (with J. Liu and Y. Wang) Journal of Differential Equations , 187 (2003), 473-493.
Standing waves with a critical frequency for nonlinear Schrodinger equations , (with J. Byeon) Archive for Rational Mechanics and Analysis , 165 (2002), 295-316.
Caffarelli-Kohn-Nirenberg inequalities with remainder terms , (with M. Willem) Journal of Functional Analysis , 203 (2003), 550-568.
Hardy inequalities with boundary terms , (with M. Zhu) , EJDEs, , Vol 2003 (2003), No 43, p 1-8.
Positive solutions to a class of quasilinear elliptic equations on $R$ , (with A. Ambrosetti) , Discrete and Continuous Dynamical Systems , 9 (2003), 55-68.
A local minimax-newton's method for finding critical points with symmetries, , (with J. Zhou) , SIAM Journal Journal on Numerical Analysis , 42 (2004), 1745-1759.
On the H\'enon equation : asymptotic profile and symmetry of ground states , (with J. Byeon) , Annales de l'Institut Henri Poincar$\acute{e}$ - Analyse non lin$\acute{e}$aire}, , 23 (2006), 803-828.
An Efficient and Stable Method for Computing Multiple Saddle Points with Symmetries, , (with J. Zhou) , SIAM Journal Journal on Numerical Analysis , 43(2005), 891-907.
Symmetry of extremal functions for the Caffarelli-Kohn-Nirenberg inequalities, , (with C.-S. Lin) , Proceedings of the American Mathematical Society , 132 (2004), 1685-1691.
Multi-bump, nodal solutions having a prescribed number of nodal domains. I. , (with Z. L. Liu) , Annales de l'Institut Henri Poincare - Analyse non lineaire , 22 (2005), 597-608.
Multi-bump, nodal solutions having a prescribed number of nodal domains. II. , (with Z. L. Liu) , Annales de l'Institut Henri Poincare - Analyse non lineaire , 22 (2005), 609-631.
Nonlinear Schr\"odinger equations with vanishing and decaying potentials , (with A. Ambrosetti) , Differential Integral Equations , 216 (2005), 78-108.
On electro-kinetic fluids: one dimensional configurations , (with C. Liu and R. Ryham) , Discrete and Continuous Dynamical Systems , B6 (2006), 357--371.
Nodal type bound states of Schr\"odinger equations via invariant set and minimax methods , (with Z. L. Liu and F. van Heerden) , Journal of Differential Equations , 214 (2005), 358-390.
Spherical semiclassical states of a critical frequency for Schr\"odinger equations with decaying potentials , (with J. Byeon) , Journal of European Mathematical Society , 8(2006), 217-228.
Multiple solutions of a superlinear elliptic equation , (with P. H. Rabinowitz and J. Su) , Rend. Lincei di Matematica , 18(2007), 97-108.
Weighted Sobolev embedding with unbounded and decaying radial potentials , (with J. Su and M. Willem) , Journal of Differential Equations , 238(2007), 201-209.
Multiple bound states of nonlinear Schr\"odinger systems , (with Z. Liu) , Communications in Mathematical Physics , 282 (2008), 721-731.
A twist condition and periodic solutions of Hamiltonian systems , (with Z. Liu and J. Su) , Advances in Mathematics , 218 (2008), 1895-1913.
Standing waves for %NLS nonlinear Schr\"odinger equations with singular potentials , (with J. Byeon) , Annales de l'Institut Henri Poincar$\acute{e}$ - Analyse non lin$\acute{e}$aire} , 26 (2009), 943-958.
Solutions of elliptic problems with nonlinearities of linear growth , (with Z. Liu and J. Su) , Calculus of Variations and Partial Differential Equations , 35 (2009), 463-480.
Ground states and bound states of a nonlinear Schr\"odinger system , (with Z. Liu) , Advanced Nonlinear Studies , 10 (2010), 175-193.
A Liouville theorem, a-priori bounds, and bifurcating branches of positive solutions for a nonlinear Schr\"odinger system , (with T. Bartsch and N. Dancer) , Calculus of Variations and Partial Differential Equations , 37 (2010), 345--361.
Multiple solitary waves of nonlinear Schr\"odinger systems , (with R. Tian) , Topological Methods in Nonlinear Analysis , 37 (2011), 203-223.
On the multiple existence of semi-positive solutions for a nonlinear Schrödinger system , (with Y. Sato) , Annales de l'Institut Henri Poincar$\acute{e}$ - Analyse non lin$\acute{e}$aire} , 30 (2013), 1-22.
Segregated and synchronized vector solutions for nonlinear Schrödinger systems , (with S. Peng) , Archive for Rational Mechanics and Analysis , 208 (2013), 305-339.
Partial symmetry of vector solutions for elliptic systems , (with M. Willem) , Journal d'Analyse Math\'ematiques , 122 (2014), 69-85.

Professional Memberships

American Mathematical Society

Other Professional Activities

Director of Graduate Study in Math & Stat, Utah State University, 1994 - 1997

Contact Information

Zhi-Qiang Wang
Department of Mathematics and Statistics
Utah State University
Logan, UT 84322

Office Phone:435 797-3529
Fax: 435 797-1822

E-Mail: zhi-qiang.wang@usu.edu

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