Curriculum Vitae of Dr. Shibo Liu


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I got my Ph.D in 2003 from Institute of Mathematics, Chinese Academy of Sciences, under the supervision of Professor Shujie Li.

Currently I am an associate professor of mathematics at Florida Institute of Technology. Before August 2022, I was a professor of mathematics at Xiamen University in China.

Research Interests

Nonlinear Analysis, Variational Methods, Nonlinear Differential Equations

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Professional Experiences

Educational Background

Research and Services

Research Grants

Publications in Peer-Reviewed Journals

[1]   S. Liu, C. Zhao, Indefinite schrödinger equation with nonlinearity sublinear at zero, Complex Variables and Elliptic Equations, 69 (2024) 1870–1885.

[2]   S. Liu, K. Perera, Multiple solutions for \((p,q)\)-Laplacian equations in \(\Bbb R^N\) with critical or subcritical exponents, Calc. Var. Partial Differential Equations, 63 (2024) Paper No. 199, 15.

[3]   L.-F. Yin, S. Liu, Solutions for quasilinear Schrödinger equation on \(\Bbb R^N\) involving indefinite potentials, Complex Var. Elliptic Equ., 69 (2024) 924–939.

[4]   S. Liu, Multiple solutions for-laplacian equations with nonlinearity sublinear at zero, Bulletin of the Australian Mathematical Society, (2024) 1–9.

[5]   S. Liu, Infinitely many solutions for schrödinger–poisson systems and schrödinger–kirchhoff equations, Mathematics, 12 (2024) 2233.

[6]   S. Liu, Gagliardo-Nirenberg-Sobolev inequality: an induction proof, Amer. Math. Monthly, 130 (2023) 859–861.

[7]   S. Jiang, S. Liu, Infinitely many solutions for indefinite Kirchhoff equations and Schrödinger-Poisson systems, Appl. Math. Lett., 141 (2023) Paper No. 108620, 7.

[8]   S. Jiang, S. Liu, Standing waves for 6-superlinear Chern-Simons-Schrödinger systems with indefinite potentials, Nonlinear Anal., 230 (2023) Paper No. 113234, 12.

[9]   S. Liu, L.-F. Yin, Quasilinear Schrödinger equations with concave and convex nonlinearities, Calc. Var. Partial Differential Equations, 62 (2023) Paper No. 100, 14.

[10]   S. Jiang, S. Liu, Multiple solutions for Schrödinger-Kirchhoff equations with indefinite potential, Appl. Math. Lett., 124 (2022) Paper No. 107672, 9.

[11]   S. Liu, On quasilinear elliptic problems with finite or infinite potential wells, Open Math., 19 (2021) 971–989.

[12]   S. Liu, S. Mosconi, On the Schrödinger-Poisson system with indefinite potential and 3-sublinear nonlinearity, J. Differential Equations, 269 (2020) 689–712.

[13]   W. Zheng, W. Gan, S. Liu, Existence of positive ground state solutions of Schrödinger-Poisson system involving negative nonlocal term and critical exponent on bounded domain, Bound. Value Probl., (2019) Paper No. 185, 10.

[14]   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.

[15]   W. Gan, S. Liu, Multiple positive solutions of a class of Schrödinger-Poisson equation involving indefinite nonlinearity in \(\Bbb {R}^3\), Appl. Math. Lett., 93 (2019) 111–116.

[16]   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.

[17]   S. Liu, J. Zhou, Standing waves for quasilinear Schrödinger equations with indefinite potentials, J. Differential Equations, 265 (2018) 3970–3987.

[18]   S. Liu, Y. Zhang, On the change of variables formula for multiple integrals, J. Math. Study, 50 (2017) 268–276.

[19]   S. Liu, Y. Wu, Standing waves for 4-superlinear Schrödinger-Poisson systems with indefinite potentials, Bull. Lond. Math. Soc., 49 (2017) 226–234.

[20]   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.

[21]   Y. Wu, S. Liu, Existence and multiplicity of solutions for asymptotically linear Schrödinger-Kirchhoff equations, Nonlinear Anal. Real World Appl., 26 (2015) 191–198.

[22]   S. Chen, S. Liu, Standing waves for 4-superlinear Schrödinger-Kirchhoff equations, Math. Methods Appl. Sci., 38 (2015) 2185–2193.

[23]   H. Chen, S. Liu, Standing waves with large frequency for 4-superlinear Schrödinger-Poisson systems, Ann. Mat. Pura Appl. (4), 194 (2015) 43–53.

[24]   S. Liu, Z. Shen, Generalized saddle point theorem and asymptotically linear problems with periodic potential, Nonlinear Anal., 86 (2013) 52–57.

[25]   C. Li, S. Liu, Homology of saddle point reduction and applications to resonant elliptic systems, Nonlinear Anal., 81 (2013) 236–246.

[26]   S. Liu, On superlinear Schrödinger equations with periodic potential, Calc. Var. Partial Differential Equations, 45 (2012) 1–9.

[27]   Z. Shen, S. Liu, On asymptotically linear elliptic equations in \(\Bbb R^N\), J. Math. Anal. Appl., 392 (2012) 83–88.

[28]   J. Sun, S. Liu, Nontrivial solutions of Kirchhoff type problems, Appl. Math. Lett., 25 (2012) 500–504.

[29]   S. Liu, Multiple periodic solutions for non-linear difference systems involving the \(p\)-Laplacian, J. Difference Equ. Appl., 17 (2011) 1591–1598.

[30]   S. Liu, On the regularity of operators near a regular operator, Amer. Math. Monthly, 117 (2010) 927–928.

[31]   C. O. Alves, S. Liu, On superlinear \(p(x)\)-Laplacian equations in \({\bf R}^N\), Nonlinear Anal., 73 (2010) 2566–2579.

[32]   S. Liu, On superlinear problems without the Ambrosetti and Rabinowitz condition, Nonlinear Anal., 73 (2010) 788–795.

[33]   S. Liu, On ground states of superlinear \(p\)-Laplacian equations in \({\bf R}^N\), J. Math. Anal. Appl., 361 (2010) 48–58.

[34]   S. Liu, Nontrivial solutions for elliptic resonant problems, Nonlinear Anal., 70 (2009) 1965–1974.

[35]   F. Fang, S. Liu, Nontrivial solutions of superlinear \(p\)-Laplacian equations, J. Math. Anal. Appl., 351 (2009) 138–146.

[36]   S. Liu, E. Medeiros, K. Perera, Multiplicity results for \(p\)-biharmonic problems via Morse theory, Commun. Appl. Anal., 13 (2009) 447–455.

[37]   S. Liu, Multiple solutions for elliptic resonant problems, Proc. Roy. Soc. Edinburgh Sect. A, 138 (2008) 1281–1289.

[38]   S. Liu, Remarks on multiple solutions for elliptic resonant problems, J. Math. Anal. Appl., 336 (2007) 498–505.

[39]   S. Liu, Multiple solutions for coercive \(p\)-Laplacian equations, J. Math. Anal. Appl., 316 (2006) 229–236.

[40]   J. Liu, S. Liu, The existence of multiple solutions to quasilinear elliptic equations, Bull. London Math. Soc., 37 (2005) 592–600.

[41]   S. Liu, S. Li, Existence of solutions for asymptotically ‘linear’ \(p\)-Laplacian equations, Bull. London Math. Soc., 36 (2004) 81–87.

[42]   S. Liu, S. Li, Critical groups at infinity, saddle point reduction and elliptic resonant problems, Commun. Contemp. Math., 5 (2003) 761–773.

[43]   S. Liu, S. Li, An elliptic equation with concave and convex nonlinearities, Nonlinear Anal., 53 (2003) 723–731.

[44]   S. B. Liu, S. J. Li, Infinitely many solutions for a superlinear elliptic equation, Acta Math. Sinica (Chinese Ser.), 46 (2003) 625–630.

[45]   Z. Zhang, S. Li, S. Liu, W. Feng, On an asymptotically linear elliptic Dirichlet problem, Abstr. Appl. Anal., 7 (2002) 509–516.

[46]   S. Liu, M. Squassina, On the existence of solutions to a fourth-order quasilinear resonant problem, Abstr. Appl. Anal., 7 (2002) 125–133.

[47]   S. Liu, Existence of solutions to a superlinear \(p\)-Laplacian equation, Electron. J. Differential Equations, (2001) No. 66, 6.

Selected Recent Invited Talks in Conferences and Seminors

Teaching