____________________________________________________________________________________________________Dr. Shibo Liu (Lau) is an associate professor of mathematics at Florida Institute of Technology. Before July 2022, he was a
full professor of mathematics at Xiamen University.
Update: November 9, 2024
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1. Research Interests
- Nonlinear Functional Analysis
- Variational Methods, Critical Point Theory
- Nonlinear Elliptic Partial Differential Equations
- Differential Geometry
- Mathematical Analysis
Welcome to contact me if you are interested to work with me for your MSc or PhD degree.
2. Professional Experiences
- 08.2024–Present: Department of Mathematics & Systems Engineering, Florida Institute of
Technology, Associate Professor
- 08.2022–07.2024: Department of Mathematics & Systems Engineering, Florida Institute of
Technology, Assistant Professor
- 10.2011–07.2022: Department of Mathematics, Xiamen University, Professor
- 08.2008–08.2011: Department of Mathematics, Shantou University, Professor
- 07.2005–07.2008: Department of Mathematics, Xiamen University, Associate Professor
- 07.2003–06.2005: Institute of Mathematics, Peking University, Postdoc
Supervisor: Prof. Jiaquan Liu
3. Educational Background
4. Teaching
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In recent semesters, I taught the following courses at Florida Institute of Technology:
- Intro to PDE & Apps
- Topology
- Real Analysis 1
- Calculus 3
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In spring 2020, I taught the following courses at Xiamen University Malaysia:
- Mathematical Analysis II
- Ordinary Differential Equations
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Dring Sep 2005 to Jul 2022, I taught various courses at Xiamen University and Shantou University in China
for undergraduate and graduate students majoring in mathematics, such as:
– Mathematical Analysis
– Real Analysis
– Partial Differential Equations
– Differential Geometry
– Nonlinear Functional Analysis
– Topology
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Teaching Related Publications
5. Research
5.1. Selected Publications
Click here for a complete list of my publications record in MathSciNet.
- S. Liu, K. Kanishka, Multiple solutions for \((p, q)\)-Laplacian equations in \(\mathbb {R}^N\) with critical or subcritical
exponents, Calc. Var. Partial Differential Equations, 63 (2024) Paper No. 199, 15.
- S. Liu, Gagliardo-Nirenberg-Sobolev inequality: an induction proof, Amer. Math. Monthly, 130
(2023) 859–861.
- S. Liu, L.-F. Yin, Quasilinear Schrödinger equations with concave and convex nonlinearities, Calc.
Var. Partial Differential Equations, 62 (2023) Paper No. 100, 14.
- S. Jiang, S. Liu, Multiple solutions for Schrödinger-Kirchhoff equations with indefinite potential,
Appl. Math. Lett., 124 (2022) Paper No. 107672, 9.
- S. Liu, S. Mosconi, On the Schrödinger-Poisson system with indefinite potential and 3-sublinear
nonlinearity, J. Differential Equations, 269 (2020) 689–712.
- S. Liu, Z. Zhao, Solutions for fourth order elliptic equations on \(\Bbb {R}^N\) involving \(u\Delta (u^2)\) and sign-changing
potentials, J. Differential Equations, 267 (2019) 1581–1599.
- P. Liu, S. Liu, On the surjectivity of smooth maps into Euclidean spaces and the fundamental
theorem of algebra, Amer. Math. Monthly, 125 (2018) 941–943.
- S. Liu, J. Zhou, Standing waves for quasilinear Schrödinger equations with indefinite potentials, J.
Differential Equations, 265 (2018) 3970–3987.
- S. Liu, Y. Wu, Standing waves for 4-superlinear Schrödinger-Poisson systems with indefinite
potentials, Bull. Lond. Math. Soc., 49 (2017) 226–234.
- S. Liu, Y. Zhang, On the change of variables formula for multiple integrals, J. Math. Study, 50
(2017) 268–276.
- A. Iannizzotto, S. Liu, K. Perera, M. Squassina, Existence results for fractional \(p\)-Laplacian
problems via Morse theory, Adv. Calc. Var., 9 (2016) 101–125.
- H. Chen, S. Liu, Standing waves with large frequency for 4-superlinear Schrödinger-Poisson
systems, Ann. Mat. Pura Appl. (4), 194 (2015) 43–53.
- C. Li, S. Liu, Homology of saddle point reduction and applications to resonant elliptic systems,
Nonlinear Anal., 81 (2013) 236–246.
- S. Liu, Z. Shen, Generalized saddle point theorem and asymptotically linear problems with periodic
potential, Nonlinear Anal., 86 (2013) 52–57.
- S. Liu, On superlinear Schrödinger equations with periodic potential, Calc. Var. Partial Differential
Equations, 45 (2012) 1–9.
- C. O. Alves, S. Liu, On superlinear \(p(x)\)-Laplacian equations in \({\bf R}^N\), Nonlinear Anal., 73 (2010) 2566–2579.
- S. Liu, On the regularity of operators near a regular operator, Amer. Math. Monthly, 117 (2010)
927–928.
- S. Liu, Nontrivial solutions for elliptic resonant problems, Nonlinear Anal., 70 (2009) 1965–1974.
- S. Liu, Multiple solutions for elliptic resonant problems, Proc. Roy. Soc. Edinburgh Sect. A, 138
(2008) 1281–1289.
- S. Liu, Remarks on multiple solutions for elliptic resonant problems, J. Math. Anal. Appl., 336 (2007)
498–505.
- S. Liu, Multiple solutions for coercive \(p\)-Laplacian equations, J. Math. Anal. Appl., 316 (2006)
229–236.
- S. Liu, S. Li, Critical groups at infinity, saddle point reduction and elliptic resonant problems,
Commun. Contemp. Math., 5 (2003) 761–773.
- S. Liu, Existence of solutions to a superlinear \(p\)-Laplacian equation, Electron. J. Differential Equations,
(2001) No. 66, 6.
5.2. Research Grants
As Principle Investigator (PI), I have conducted 4 research projects funded by Natural Science Foundation of China
(NSFC).
- Quasilinear Schrödinger equations with indefinite potential and related problems, NSFC grant
(12071387), 01.2021–12.2024. (PI)
Terminated in July 2022 (because I left China to continue my career in the USA)
- Standing waves for nonlinear Schrödinger-Poisson systems with high frequency and related
problems, NSFC grant (11671331), 01.2017–12.2020. (PI)
- Critical point theory and nonlinear Schrödinger-Poisson systems, Distinguished Young Scholar
Foundation of Fujian grant (2014J06002), 01.2014–12.2016. (PI)
- Strongly indefinite and noncompact variational problems, NSFC grant (11171204), 01.2012–12.2015.
(PI)
- Critical groups and multiple solutions of nonlinear differential equations, NSFC grant (10601041),
01.2007–12.2009. (PI)
- Program for New Century Excellent Talents in Fujian Province University, 1.2008–12.2010. (PI)
6. Selected Presentations
- Multiple solutions for 1-D quasilinear indefinite Schrödinger equations, International Conference
on Differential Equations, May 31 — June 2, 2024, Florida Gulf Coast University, Fort Myers, FL, USA
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Surjections between Euclidean Spaces, Changing Variables and Brouwer Fixed Point Theorem
- Annual Joint Meetings of the MAA-Florida Section and FTYCMA, Feb 23–24, 2024, Florida Gulf
Coast University, Fort Myers, FL, USA (Slides)
- Florida Institute of Technology, Jan 25, 2024, Melbourne, FL, USA (Video)
- Tianyuan Mathematical Center in Southeast China (TMSE), Dec 11, 2022, Xiamen, China (Slides
and Video, both are in Chinese)
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13th AIMS International Conference on Dyn. Systems, Diff. Equations and Applications, May 31–June 4,
2023, University of North Carolina at Wilmington, NC, USA
- Stationary Schrödinger Type Equations with Nonlinearities Sublinear at Zero
- Nontrivial Solutions for Indefinite Schrödinger Type Equations
- An introduction to variational methods for nonlinear differential equations, Florida Institute of Technology,
Apr 14, 2023, Melbourne, FL, USA
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Morse theory and nonlinear Schrödinger equations,
- University of Alabama, Apr 21, 2023, Tuscaloosa, AL, USA
- Georgia Southern University, Mar 24, 2023, Statesboro, GA, USA
- Florida Institute of Technology, Jan 20, 2023, Melbourne, FL, USA
- Local linking and its applications to indefinite Schrödinger equations, Universidade de Brasília, Feb 18,
2022 (Online)
- Nonlinear Schrödinger-Poisson systems with indefinite potentials. 9th International Conference on
Differential Equations and Dynamical Systems, May 2015, Texas A & M University of Commerce, Dallas,
USA
- Standing waves of nonlinear Schrödinger equations and Schrödinger-Poisson systems, The \(17^{\mathrm {th}}\) National
Conference on Nonlinear Functional Analysis, Oct 2012, Jiangsu Normal University, Xuzhou,
China
- Critical groups under saddle point reduction and elliptic resonant problems with variable coefficients, The \(16^{\mathrm {th}}\)
National Conference on Nonlinear Functional Analysis, Nov 2010, Xiamen University, Xiamen,
China
- Lyapunov-Schmidt reduction, critical groups and mulltiple solutions of elliptic resonant problems, 7th AIMS
International Conference on Dyn. Systems, Diff. Equations and Applications, May 2008, University of Texas at
Arlington, Arlington, TX, USA
- Critical groups and existence of solutions for \(p\)-Laplacian equations, The \(13^{\mathrm {th}}\) National Conference on Nonlinear
Functional Analysis, Apr 2003, Yangzhou University, Yangzhou, China
- Critical groups at infinity, saddle point reduction and elliptic resonant problems, Satellite Conference on
Nonlinear Functional Analysis, ICM 2002, Aug 2002, Shanxi University, Taiyuan, China
7. LaTeX & Web-Pages
I am an expert on LaTeX, who can solve problems in using LaTeX with simple idea.
8. Non-Professional Activities
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Guitar: When I was young I admired Guitarist. Now I am not young and I have started playing Guitar.
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Karaoke: I can sing in Mandarin, Cantonese, Hokkien, Teochew, and English.
Some songs I sang can be found at
- Marathon (long-distance running)
- Basketball, Table tennis, Hiking,…