$\int$

Shibo Liu (1975.11--), Ph.D Professor of Mathematics email: liusb@xmu.edu.cn URL: http://www.liusb.com

Research Area

Nonlinear Analysis, Nonlinear Differential Equations

Professional Experience

• 2011.10--present, Professor, Xiamen University.

• 2008.8-2011.8, Professor, Shantou University.

• 2005.7-2008.7, Associate Professor, Xiamen University.

• 2003.7-2005.6, Postdoc Fellow, Peking University.

Education Experience

• 2000.9-2003.6, Ph.D., Institute of Mathematics, Chinese Academy of Sciences, Beijing China.

• 1997.9-2000.6, M.Sc., Department of Mathematics, Lanzhou University, Lanzhou China.

• 1993.9-1997.6, B.Sc., M.Sc., Department of Mathematics, Lanzhou University, Lanzhou China.

Teaching

Mathematical Analysis, Real Analysis, Topology, Partial Differential Equations, Differential Geometry.

Research Grants and Honors

1. Strongly indefinite and noncompact variational problems, NSFC grant 11171204, 2012.1-1015.12, PI.

2. Critical groups and multiple solutions of nonlinear differential equations, NSFC grant 10601041, 2007.1-2009.12, PI.

Selected Publications

1. S.B. Liu, On suplinear Schrödinger equations with periodic potential, Calc. Var. Partial Differential Equations, (2012) in press.

2. S.B. Liu, Multiple periodic solutions for nonlinear difference systems involving the $p$-Laplacian, J. Differ. Equ. Appl., 17 (2011), 1591-1598.

3. C.O. Alves, S.B. Liu, On superlinear $p(x)$-Laplacian equations in $\mathsf{R}^{N}$, Nonlinear Anal., 73 (2010), 2566-2579.

4. S.B. Liu, On the regularity of operators near regular operator, Amer. Math. Monthly, 117 (2010), 927-928.

5. S.B. Liu, Nontrivial solutions for elliptic resonant problems, Nonlinear Anal., 70 (2009), 1965-1974.

6. S.B. Liu, Multiple solutions for elliptic resonant problems, Proc. Roy. Soc. Edinburgh, 138 (2008), 1281-1289.

7. S.B. Liu, Remarks on multiple solutions for elliptic resonant problems, J. Math. Anal. Appl., 336 (2007), 498-505.

8. S.B. Liu, Multiple solutions for coercive $p$-Laplacian equations, J. Math. Anal. Appl., 316 (2006), 229-236.

9. S.B. Liu, S.J. Li, Existence of solutions for asymptotically `linear' $p$-Laplacian equations, Bull. London Math. Soc., 36 (2004), 81-87.

10. S.B. Liu, S.J. Li, Critical groups at infinity, saddle point reduction and elliptic resonant problems, Commun. Contemp. Math., 5 (2003), 761-773.

Conference and Visits

1. The $16^{\mathrm{th}}$ National Conference on Nonlinear Functional Analysis, 2010.11, Xiamen China.

   Title: Critical groups under saddle point reduction and elliptic resonant problems with variable coefficients.

2. 7th AIMS International Conference on Dyn. Systems, Diff. Equations and Applications, 2008.5, Arlington Texas USA.

   Title: Lyapunov-Schmidt reduction, critical groups and mulltiple solutions of elliptic resonant problems.

3. Workshop and Conference on Recent Trends in Nonlinear Variational Problems, 2003.4, Abdus Salam ICTP, Trieste Italy.

4. Satellite Conference on Nonlinear Functional Analysis, ICM 2002, 2002.8, Taiyuan, China.

   Title: Critical groups at infinity, saddle point reduction and elliptic resonant problems.

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