Riccardo Molle

Professor of Mathematical Analysis




Research Interests

My research activity concerns nonlinear Partial Differential Equations and systems of elliptic type, coming from physic and geometrical problems.
The methods used are typical of nonlinear analysis: min-max methods, concentration-compactness, Lusternik-Schnirelmann category, degree theory, barycenter maps, minimization methods.

Selected topics

  • prescribed mass problems;
  • Schrödinger-Poisson systems;
  • Choquard equations;
  • the Bahri-Lions conjecture;
  • existence of infinitely many solutions for nonlinear Schrödinger equations;
  • analysis of the Fučík spectrum;
  • critical and supercritical nonlinearities in bounded and unbonded domains;
  • variational inequalities.




    • Publications from 2013


    Updated January 2025

  • R. Molle - V. Moroz - G. Riey, Normalised solutions and limit profiles of the defocusing Gross--Pitaevskii--Poisson equation,
    arXiv:2308.04527, submitted for publication.


  • R. Molle - D. Passaseo, Uniqueness of solutions for nonlinear elliptic problems with supercritical growth in ramified domains,
     to appear on "Communications in Contemporary Mathematics", doi: 10.1142/S0219199724500330.


  • L. Guo - Q. Li - X. Luo - R. Molle, Standing waves for two-component elliptic system with critical growth in R4: the attractive case,
    arXiv:2211.03425, Math. Z. 309 (2025), no. 2, art. 38, 40 pp.

  • R. Molle - D. Passaseo, Nonexistence results for elliptic problems with supercritical growth in thin planar domains,
     Nonlinear Differ. Equ. Appl. 30 (2023), art. 66, 23 pp. doi: 10.1007/s00030-023-00875-7.

  • S. Lancelotti - R. Molle, Normalized positive solutions for Schrödinger equations with potentials in unbounded domains,
    arXiv:2208.12090, Proceedings A of the Royal Society of Edinburgh 154 (2024), no. 5, 1518-1551.

  • R. Molle - D. Passaseo, On the Bahri-Lions conjecture for elliptic equations with non-symmetric nonlinearities,
     Calc. Var. Partial Differential Equations, doi: 10.1007/s00526-023-02507-5.

  • R. Molle - A. Sardilli, On a planar Schrödinger-Poisson system involving a non-symmetric potential,
    arXiv:2206.01941, Proc. Edinb. Math. Soc. (2) 65 (2022), no. 4, 1133–1146.

  • R. Molle - D. Passaseo, Infinitely many solutions for elliptic equations with non-symmetric nonlinearities,
    arXiv:2112.02298, Calc. Var. Partial Differential Equations 61 (2022), no. 3, Art. 115, 26 pp.

  • R. Molle - G. Riey - G. Verzini, Existence of normalized solutions to mass supercritical Schrödinger equations with negative potential,
    arXiv:2104.12834, J. Differential Equations 333 (2022), 302-331.

  • C.O. Alves - G.M. Figueiredo - R. Molle, Multiple positive bound state solutions of a critical Choquard equation,
    arXiv:1812.04875, Discrete Contin. Dyn. Syst. 41 (2021), no. 10, 4887-4919.

  • T. Bartsch - R. Molle - M. Rizzi - G. Verzini, Normalized solutions of mass supercritical Schrödinger equations with potential,
    arXiv:2008.07431, Comm. Partial Differential Equations 46 (2021), no. 9, 1729-1756.

  • R. Molle - D. Passaseo, Uniqueness of solutions for nonlinear Dirichlet problems with supercritical growth,
    arXiv:1912.12243, Topol. Methods Nonlinear Anal. 57 (2021), no. 2, 535-546.

  • R. Molle - D. Passaseo, Infinitely many positive solutions of nonlinear Schrödinger equations,
    arXiv:1912.12254, Calc. Var. Partial Differential Equations 60 (2021), no. 2, Paper No. 79, 35 pp.

  • R. Molle - D. Passaseo, Nonexistence of solutions for Dirichlet problems with supercritical growth in tubular domains,
    arXiv:1905.08467, Adv. Nonlinear Stud. 21-1, 189-198, 2021.

  • S. Lancelotti - R. Molle, Positive solutions for autonomous and non-autonomous nonlinear critical elliptic problems in exterior domains,
    arXiv:1802.025, Nonlinear Differ. Eq. Appl. 27, Art. 8, 28 pp, 2020.

  • R. Molle - D. Passaseo, Nonexistence of solutions for elliptic equations with supercritical nonlinearity in nearly nontrivial domains,
    arXiv:1902.02314, Rend. Lincei Mat. Appl. 31, 121-130, 2020.

  • G. Cerami - R. Molle, Multiple positive bound states for critical Schrödinger-Poisson systems,
    arXiv:1802.02539, ESAIM Control Optim. Calc. Var. 25, Art. 73, 29 pp, 2019.

  • G. Cerami - R. Molle, Infinitely many positive standing waves for Schrödinger equations with competing coefficients,
    arXiv:1805.10193, Comm. in PDE 44-2, 73-109, 2019; DOI: 10.1080/03605302.2018.154190 (2018).

  • G. Cerami - R. Molle, Positive bound state solutions for some Schrödinger-Poisson systems,
    Nonlinearity 29-10, 3103-3119, 2016.

  • R. Molle - D. Passaseo, Infinitely many new curves of the Fučík spectrum,
    Ann. Inst. H. Poincaré Anal. Non Linéaire 32-6, 1145-1171, 2015.

  • R. Molle - D. Passaseo, Variational properties of the first curve of the Fučík spectrum for elliptic operators,
    Calc. Var. and PDE 54-4, 3735--3752, 2015.

  • R. Molle - D. Passaseo, Multiplicity of solutions of nonlinear scalar field equations,
    Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 26, pp. 75-82, 2015.

  • G. Cerami - R. Molle - D. Passaseo, Multiplicity of positive and nodal solutions for scalar field equations,
    arXiv:1310.7907, J. Differential Equations 257-10, 3554-3606, 2014.

  • R. Molle - D. Passaseo, On the first curve of the Fučík spectrum for elliptic operators,
    Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 25-2, 141-146, 2014.

  • R. Molle - D. Passaseo, Elliptic equations with jumping nonlinearities involving high eigenvalues,
    Calc. Var. and PDE 49-1/2, 861-907, 2014.

  • R. Molle - D. Passaseo, New properties of the Fučík spectrum,
    C. R. Math. Acad. Sci. Paris 351-17/18, 681-685, 2013.