Andrei Stan

Current position:

Scientific researcher III  at Tiberiu Popoviciu Institute of Numerical Analysis

Interests:

  • Partial Differential Equations
  • Nonlinear Analysis
  • Numerical Analysis

Date and Place of Birth

Câmpeni (Alba), 1997

Education and degrees

2021-2024: Ph.D. Student in Mathematics, Nonlinear Analysis.Scientific advisor: Prof. dr.  Radu Precup

2019-2021: Master Degree in Advanced Mathematics, Babeș-Bolyai University, Cluj-Napoca

2016-2019: Bachelor Degree in Mathematics and Computer Science, Babeș-Bolyai University, Cluj-Napoca

2012-2016, Avram Iancu National College, Câmpeni

Employment history

2025-present: scientific researcher III at ICTP

2021-2025: Research assistant at ICTP

Talks at Conferences

  • Numerical Analysis, Numerical Modeling, Approximation Theory (NA-NM-AT 2025), Nash equilibria of fractional functionals via a Dinkelbach–Ekeland type approach, Cluj-Napoca, Romania, 3–6 November 2025.
    https://ictp.acad.ro/nanmat/nanmat-2025/

  • The First Balkan Workshop on Fixed Point Theory and Applications, Fixed point results and the Ekeland variational principle in vector B-metric spaces, Babeș-Bolyai University, Cluj-Napoca, Romania, 12–14 June 2025.
    https://www.cs.ubbcluj.ro/1st-balkan-workshop-on-fixed-point-theory/

  • Recent Advances in Nonlinear Differential Problems and Applications, Localization of critical points in conical sets via the method of Nehari manifolds, Perugia, Italy, 4–6 June 2025.
    https://analisi.sites.dmi.unipg.it/Randpa2025/program.htm

  • Numerical Analysis, Numerical Modeling, Approximation Theory (NA-NM-AT 2023), Localization of Nash equilibria for systems with partial variational structure, Cluj-Napoca, Romania, 6–10 November 2023.
    https://ictp.acad.ro/nanmat/nanmat-2023/

  • The 14th International Conference on Fixed Point Theory and its Applications, Nash equilibria for nonpotential systems, Brașov, Romania, 11–14 July 2023.
    https://icfpta2023.files.wordpress.com/2023/07/icfpta_2023-abstractbook-v7.pdf

  • The 14th Joint Conference on Mathematics and Computer Science, On the existence of Nash equilibria for nonvariational systems, Cluj-Napoca, Romania, 24–27 November 2022.
    https://www.cs.ubbcluj.ro/~macs/2022/index.php?m=2

  • XVème Colloque Franco-Roumain de Mathématiques Appliquées, Existence and localization of Nash equilibria for systems with partial variational structure, Toulouse, France, 29 August – 2 September 2022.
    https://15colfrro.sciencesconf.org

  • Fourth Romanian Itinerant Seminar on Mathematical Analysis and its Applications (RISMAA), Localization of Nash-type equilibria for systems with a partial variational structure, Brașov, Romania, 19–21 May 2022.
    https://mateinfo.unitbv.ro/ro/136-conferin%C8%9Be-category/507-rismaa-about

  • Zilele Academice Clujene, 70 de ani de la înființarea Institutului de calcul „Tiberiu Popoviciu” (28.10.2021), Cluj-Napoca.
  • International Student Conference StudMath-IT (11.2020), Arad (online).

Computer experience

  • Programming languages: Matlab, Julia, PHP (CakePHP, Laravel), Python.

Scientific articles:

  1. Precup, R., Stan, A. Existence, Uniqueness, and Localization Results for a Dirichlet Problem in Geophysics. J. Math. Fluid Mech. 28, 72 (2026). https://doi.org/10.1007/s00021-026-01061-2
  2. Malina, A., Stan, A. Componentwise localization of positive periodic solutions for a general Bazykin-type system. Nonlinear Anal. Real World Appl. 94, 104701 (2027)
  3. Fernández–Pardo, L. M., Rodríguez–López, J., Stan, A. Hybrid Nehari-Krasnosel’skiĭ type results and applications. J. Differ. Equ. 476, 114481 (2026).
  4. A. Stan, Two abstract methods of lower and upper solutions with applications, Results Math 81, 69 (2026)
  5. R. Precup, A. Stan, A Nehari manifold method for nonvariational problems (Preprint), 2025.
  6. R. Precup, A. Stan, Hybrid Nehari-Schauder type fixed point results and applications (Preprint),  J. Fixed Point Theory Appl. 28, 15 (2026)..
  7. A. Stan, Symmetric Water Waves with Surface Tension: Traveling Wave Behavior and Maximal Horizontal Velocity, Water Waves, 2025. 
  8. A. Stan, Free-surface equatorial flows with surface tension in spherical coordinates, Applicable Analysis, 2025. https://doi.org/10.48550/arXiv.2412.04763
  9. R. Precup, A. Stan Critical point localization and multiplicity results in Banach spaces via Nehari manifold technique, Preprint, 2025. https://doi.org/10.48550/arXiv.2505.08678
  10. R. Precup, A. Stan, A mutual control problem for semilinear system via fixed point approach, J. Nonlinear Convex Anal., 26(2025), no. 5, 1081-1094.
  11. A. Stan Localization of critical points in annular conical sets via the method of Nehari manifold,  Mediterr. J. Math. 23, 62 (2026).
  12. R. Precup, A. Stan, Du, W.-S. Control of Semilinear Differential Equations with Moving Singularities Spaces, Fractal Fract., 2025. https://doi.org/10.3390/fractalfract9040198
  13. R. Precup, A. Stan, Fixed Point Results and the Ekeland Variational Principle in Vector B-Metric Spaces, Axioms, 2025. https://doi.org/10.3390/axioms14040250
  14. A. Stan, Role of partial functionals in the study of variational, Topological Methods in Nonlinear Analysis, 65 (2025) no. 1, pp. 383 – 399.  https://doi.org/10.12775/TMNA.2024.033  
  15. C. Gheorghe, A. Stan, Stratified equatorial flows in cylindrical coordinates with surface tension, Monatsh. Math., 205 (2024), 497–509. https://doi.org/10.1007/s00605-024-02007-4
  16. R. Precup, A. Stan, On equilibrium in control problems with applications to evolution systems, Preprint, 2024. arXiv:2409.09805.. 
  17. A. Stan, Localization of Nash-type equilibria for systems with partial variational structure, J. Numer. Anal. Approx. Theory, 52 (2023) no. 2, pp. 253-272, https://doi.org/10.33993/jnaat522-1356.
  18. R. Precup, A. Stan, Linking methods for componentwise variational systems, Results Math. 78 (2023) 246, https://doi.org/10.1007/s00025-023-02026-x
  19. A. Stan, Nash equilibria for componentwise variational systems, Journal of Nonlinear Functional Analysis, 2023 (2023), art. no. 6, http://jnfa.mathres.org/archives/3029
  20. R. Precup, A. Stan, Stationary Kirchhoff equations and systems with reaction terms, AIMS Mathematics, 7 (2022) no. 8, pp. 15258-15281. doi: 10.3934/math.2022836
  1. The method of Nehari manifold
  2. Relevant inequalities for localization of solutions:

    (a) Schur inequality. [Appendix I, Loukas Grafakos, Modern Fourier Analysis.]

    (b) Riesz–Thorin interpolation. A linear operator bounded on both Lᵖ and Lʳ is bounded on Lᑫ for intermediate exponents q, with the corresponding interpolated operator norm. [Folland.]

    (c) Hölder’s inequality for isotone operators. In connection with Schur’s inequality. [Theorem 4.12, J. E. Pečarić, F. Proschan and Y. L. Tong, Convex Functions, Partial Orderings, and Statistical Applications.]

    (d) Two-sided estimates for the Dirichlet Green function: cG δ(x)δ(y) ≤ G(x,y) ≤ CG δ(x)δ(y)|x−y|−n, for x ≠ y, where δ(x) = dist(x, ∂Ω). [Z. Zhao, Green function for Schrödinger operator and conditioned Feynman–Kac gauge; M. Grüter and K.-O. Widman, The Green function for uniformly elliptic equations.]

    (e) Boundary estimates for the first Dirichlet eigenfunction: ce δ(x) ≤ φ₁(x) ≤ Ce δ(x). [E. B. Davies and B. Simon, Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians.]

    (f) Weighted L¹-to-Lᵖ estimates for the Green operator: ‖Sh‖Lᵖ(Ω) ≤ Mp ∫Ω h(x)φ₁(x) dx, for 1 ≤ p < n/(n−1). [Theorem 3.1(i), M. Montenegro and A. C. Ponce, The sub-supersolution method for weak solutions, together with the comparison φ₁ ≍ δ.]

    (g) Harnack-type lower estimates for the Green operator: Sh(x) ≥ cH φ₁(x) ∫Ω h(y)φ₁(y) dy. [Consequence of the lower Green function estimate and φ₁ ≍ δ. See also Lemma 3.2, H. Brezis and X. Cabré, Some simple nonlinear PDE’s without solutions, for the boundary-distance formulation.]

  3. Useful for estimates:

    (a) L’Hôpital-type rule for monotonicity. Monotonicity of f′/g′ implies the same monotonicity of [f(x) − f(a+)]/[g(x) − g(a+)], provided g′ has a fixed nonzero sign and the endpoint limits are finite. [Theorem 1, S. Wu and L. Debnath, A generalization of L’Hôspital-type rules for monotonicity and its application, Applied Mathematics Letters 22 (2009), 284–290.]