Shibo Liu’s Homepage

Shibo Liu’s Homepage
 1.  Research Interests
 2.  Professional Experiences
 3.  Educational Background
 4.  Teaching
 5.  Research
   5.1.  Selected Publications
   5.2.  Research Grants
 6.  Selected Presentations
 7.  LaTeX & Web-Pages
 8.  Non-Professional Activities
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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: September 30, 2024

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1. Research Interests

Welcome to contact me if you are interested to work with me for your MSc or PhD degree.

2. Professional Experiences

3. Educational Background

4. Teaching

5. Research

5.1. Selected Publications

Click here for a complete list of my publications record in MathSciNet.

  1. 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.
  2. S. Liu, Gagliardo-Nirenberg-Sobolev inequality: an induction proof, Amer. Math. Monthly, 130 (2023) 859–861.
  3. S. Liu, L.-F. Yin, Quasilinear Schrödinger equations with concave and convex nonlinearities, Calc. Var. Partial Differential Equations, 62 (2023) Paper No. 100, 14.
  4. S. Jiang, S. Liu, Multiple solutions for Schrödinger-Kirchhoff equations with indefinite potential, Appl. Math. Lett., 124 (2022) Paper No. 107672, 9.
  5. S. Liu, S. Mosconi, On the Schrödinger-Poisson system with indefinite potential and 3-sublinear nonlinearity, J. Differential Equations, 269 (2020) 689–712.
  6. 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.
  7. 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.
  8. S. Liu, J. Zhou, Standing waves for quasilinear Schrödinger equations with indefinite potentials, J. Differential Equations, 265 (2018) 3970–3987.
  9. S. Liu, Y. Wu, Standing waves for 4-superlinear Schrödinger-Poisson systems with indefinite potentials, Bull. Lond. Math. Soc., 49 (2017) 226–234.
  10. S. Liu, Y. Zhang, On the change of variables formula for multiple integrals, J. Math. Study, 50 (2017) 268–276.
  11. 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.
  12. H. Chen, S. Liu, Standing waves with large frequency for 4-superlinear Schrödinger-Poisson systems, Ann. Mat. Pura Appl. (4), 194 (2015) 43–53.
  13. C. Li, S. Liu, Homology of saddle point reduction and applications to resonant elliptic systems, Nonlinear Anal., 81 (2013) 236–246.
  14. S. Liu, Z. Shen, Generalized saddle point theorem and asymptotically linear problems with periodic potential, Nonlinear Anal., 86 (2013) 52–57.
  15. S. Liu, On superlinear Schrödinger equations with periodic potential, Calc. Var. Partial Differential Equations, 45 (2012) 1–9.
  16. C. O. Alves, S. Liu, On superlinear \(p(x)\)-Laplacian equations in \({\bf R}^N\), Nonlinear Anal., 73 (2010) 2566–2579.
  17. S. Liu, On the regularity of operators near a regular operator, Amer. Math. Monthly, 117 (2010) 927–928.
  18. S. Liu, Nontrivial solutions for elliptic resonant problems, Nonlinear Anal., 70 (2009) 1965–1974.
  19. S. Liu, Multiple solutions for elliptic resonant problems, Proc. Roy. Soc. Edinburgh Sect. A, 138 (2008) 1281–1289.
  20. S. Liu, Remarks on multiple solutions for elliptic resonant problems, J. Math. Anal. Appl., 336 (2007) 498–505.
  21. S. Liu, Multiple solutions for coercive \(p\)-Laplacian equations, J. Math. Anal. Appl., 316 (2006) 229–236.
  22. S. Liu, S. Li, Critical groups at infinity, saddle point reduction and elliptic resonant problems, Commun. Contemp. Math., 5 (2003) 761–773.
  23. 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).

6. Selected Presentations

7. LaTeX & Web-Pages

I am an expert on LaTeX, who can solve problems in using LaTeX with simple idea.

8. Non-Professional Activities