Alberto SaldañaMathematics · UNAM

Research · Alberto Saldaña

Publications

Papers and preprints on nonlinear partial differential equations and related topics.

Work in progress

Preprints

  1. On Neumann p-Laplacian Lane-Emden equations and their asymptotic relationship with relative isoperimetric problems

    With S. McCurdy and D. Schiera

    arXiv:2606.08222 (2026)

    arXiv

  2. Sublinear elliptic equations with a sharp change of sign in the nonlinearity

    With M. Clapp and D. Schiera

    arXiv:2603.11766 (2026)

    arXiv

  3. The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces

    With J. C. Fernández

    arXiv:2507.21779 (2025)

    arXiv

By year

Published papers

2026

  2. Critical equations with a sharp change of sign in the nonlinearity

    With M. Clapp and J. Faya

    Discrete and Continuous Dynamical Systems 50, 46–68 (2026).

    Journal arXiv

  3. On least energy solutions to a pure Neumann Lane-Emden system: convergence, symmetry breaking, and multiplicity

    With D. Schiera and H. Tavares

    Asymptotic Analysis 149(1), 961–998 (2026).

    Journal arXiv

  4. Multiple solutions to a semilinear elliptic equation with a sharp change of sign in the nonlinearity

    With M. Clapp and A. Pistoia

    Journal de Mathématiques Pures et Appliquées 205, article 103783 (2026).

    Journal arXiv

2025

  1. Fractional Q-curvature on the sphere and optimal partitions

    With H. Chang and J. C. Fernández

    Journal of the London Mathematical Society 112(6), article e70366 (2025).

    Journal arXiv

  2. A concentration phenomenon for a semilinear Schrödinger equation with periodic self-focusing core

    With M. Clapp and A. Szulkin

    Partial Differential Equations and Applications 6(6), article 55 (2025).

    Journal arXiv

  3. FEM for 1D-problems involving the logarithmic Laplacian: error estimates and numerical implementation

    With V. Hernández-Santamaría, S. Jarohs, and L. Sinch

    Computers & Mathematics with Applications 192, 189–211 (2025).

    Journal arXiv

  4. An asymptotic relationship between Lane-Emden systems and the 1-bilaplacian equation

    With N. Abatangelo and H. Tavares

    Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, published online 7 March 2025 (forthcoming issue).

    Journal arXiv

  5. On a Schrödinger system with shrinking regions of attraction

    With M. Clapp and A. Szulkin

    Zeitschrift für angewandte Mathematik und Physik 76(1), article 37 (2025).

    Journal arXiv

  10. Differentiability of the nonlocal-to-local transition in fractional Poisson problems

    With S. Jarohs and T. Weth

    Potential Analysis 63(1), 77–99 (2025).

    Journal arXiv

2024

  1. Uniqueness and nondegeneracy of least-energy solutions to fractional Dirichlet problems

    With A. Dieb and I. Ianni

    Calculus of Variations and Partial Differential Equations 63(9), article 238 (2024).

    Journal arXiv

  2. Optimal pinwheel partitions for the Yamabe equation

    With M. Clapp and J. Faya

    Nonlinearity 37(10), article 105004 (2024).

    Journal arXiv

  3. Configuration spaces and multiple positive solutions to a singularly perturbed elliptic system

    With M. Clapp and A. Szulkin

    Boletín de la Sociedad Matemática Mexicana 30(2), article 34 (2024).

    Journal arXiv

  4. Classical solutions to integral equations with zero order kernels

    With H. Chang

    Mathematische Annalen 389(2), 1463–1515 (2024).

    Journal arXiv

2023

  1. Existence of solutions to a slightly supercritical pure Neumann problem

    With A. Pistoia and H. Tavares

    SIAM Journal on Mathematical Analysis 55(4), 3844–3887 (2023).

    Journal arXiv

  2. Uniqueness and nondegeneracy for Dirichlet fractional problems in bounded domains via asymptotic methods

    With A. Dieb and I. Ianni

    Nonlinear Analysis 236, article 113354 (2023).

    Journal arXiv

  3. Exponential decay of the solutions to nonlinear Schrödinger systems

    With F. Angeles and M. Clapp

    Calculus of Variations and Partial Differential Equations 62(5), article 160 (2023).

    Journal arXiv

  4. Small order limit of fractional Dirichlet sublinear-type problems

    With F. Angeles

    Fractional Calculus and Applied Analysis 26(4), 1594–1631 (2023).

    Journal arXiv

  5. Symmetry properties of sign-changing solutions to nonlinear parabolic equations in unbounded domains

    With T. Weth and J. Földes

    Journal of Dynamics and Differential Equations 35(3), 2691–2724 (2023).

    Journal arXiv

2022

  1. On the least-energy solutions of the pure Neumann Lane-Emden equation

    With H. Tavares

    Nonlinear Differential Equations and Applications NoDEA 29(3), article 30 (2022).

    Journal arXiv

  2. Small order asymptotics for nonlinear fractional problems

    With V. Hernández-Santamaría

    Calculus of Variations and Partial Differential Equations 61(3), article 92 (2022).

    Journal arXiv

2021

  1. Sharp asymptotic behavior of radial solutions of some planar semilinear elliptic problems

    With I. Ianni

    Journal of Differential Equations 304, 102–164 (2021).

    Journal arXiv

  4. A solution to a slightly subcritical elliptic problem with non-power nonlinearity

    With M. Clapp, R. Pardo, and A. Pistoia

    Journal of Differential Equations 275, 418–446 (2021).

    Journal arXiv

  6. On fractional higher-order Dirichlet boundary value problems: between the Laplacian and the bilaplacian

    Alberto Saldaña

    In Mexican Mathematicians in the World, edited by Fernando Galaz-García, Cecilia González-Tokman, and Juan Carlos Pardo Millán. Contemporary Mathematics 775, 255–277. American Mathematical Society (2021).

    Chapter arXiv

  7. Phase separation, optimal partitions, and nodal solutions to the Yamabe equation on the sphere

    With M. Clapp and A. Szulkin

    International Mathematics Research Notices 2021(5), 3633–3652 (2021).

    Journal arXiv

2020

  2. Entire nodal solutions to the critical Lane-Emden system

    With M. Clapp

    Communications in Partial Differential Equations 45(4), 285–302 (2020).

    Journal arXiv

  3. Sharp concentration estimates near criticality for radial sign-changing solutions of Dirichlet and Neumann problems

    With M. Grossi and H. Tavares

    Proceedings of the London Mathematical Society 120(1), 39–64 (2020).

    Journal arXiv

2019

  1. Positive powers of the Laplacian in the half-space under Dirichlet boundary conditions

    With N. Abatangelo, S. Dipierro, M.M. Fall, and S. Jarohs

    Discrete and Continuous Dynamical Systems 39(3), 1205–1235 (2019).

    Journal arXiv

2018

  1. Positive powers of the Laplacian: from hypersingular integrals to boundary value problems

    With N. Abatangelo and S. Jarohs

    Communications on Pure and Applied Analysis 17(3), 899–922 (2018).

    Journal arXiv

  3. Least energy nodal solutions of Hamiltonian elliptic systems with Neumann boundary conditions

    With H. Tavares

    Journal of Differential Equations 265(12), 6127–6165 (2018).

    Journal arXiv

2016

  1. Partial symmetry of solutions to parabolic problems via reflection methods

    Alberto Saldaña

    Rendiconti del Seminario Matematico dell’Università e del Politecnico di Torino 74(2), 105–112 (2016).

    Journal (PDF)

  2. Qualitative properties of solutions to mixed-diffusion bistable equations

    With D.Bonheure and J. Földes

    Calculus of Variations and Partial Differential Equations 55(3), article 67 (2016).

    Journal arXiv

  3. Qualitative properties of coexistence and semi-trivial limit profiles of nonautonomous nonlinear parabolic Dirichlet systems

    Alberto Saldaña

    Nonlinear Analysis 130, 31–46 (2016).

    Journal arXiv

2015

  1. On the asymptotic shape of solutions to Neumann problems for non-cooperative parabolic systems

    With T. Weth

    Journal of Dynamics and Differential Equations 27(2), 307–332 (2015).

    Journal arXiv

2012

  1. Asymptotic axial symmetry of solutions of parabolic equations in bounded radial domains

    With T. Weth

    Journal of Evolution Equations 12(3), 697–712 (2012).

    Journal arXiv

Doctoral research

Ph.D. thesis

  1. Partial symmetries of solutions to nonlinear elliptic and parabolic problems in bounded radial domains

    Alberto Saldaña

    PhD thesis, Johann Wolfgang Goethe-Universität Frankfurt am Main, Germany, 2014

    Thesis (PDF)