sample of publications

• articles 

  • Bound and ground states of coupled 'NLS-KdV' equations with Hardy potential and critical power.  Journal of Differential Equations.  365:560-590. 2023
  • Nonlinear Fractional Schrödinger Equations coupled by power-type nonlinearities.  Advances in Differential Equations.  28:113-142. 2023
  • Existence of bound and ground states for an elliptic system with double criticality.  NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS.  216:1-26. 2022
  • Regularity of solutions to a fractional elliptic problem with mixed Dirichlet-Neumann boundary data.  Advances in Calculus of Variations.  14:521-539. 2021
  • Existence of positive solutions for a Brezis-Nirenberg type problems involving an inverse operator.  Electronic Journal of Differential Equations.  2021:1-24. 2021
  • How to divide exactly in Mathematics.  Preprint.  1-3. 2020
  • Semilinear fractional elliptic problems with mixed Dirichlet-Neumann boundary conditions.  Fractional Calculus and Applied Analysis.  23:1208-1239. 2020
  • Positive solutions for semilinear fractional elliptic problems involving an inverse fractional operator.  NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS.  51:1-21. 2020
  • The Brezis-Nirenberg problem for the fractional Laplacian with mixed Dirichlet-Neumann boundary conditions.  JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS.  473:1002-1025. 2019
  • Perturbed Problems Involving the Square Root of the Laplacian.  Minimax Theory and its Applications.  4:33-54. 2019
  • A higher order system of some coupled nonlinear Schrödinger and Korteweg-de Vries equations.  JOURNAL OF MATHEMATICAL PHYSICS.  58:111503-1-111503-13. 2017
  • On the existence of bound and ground states for some coupled nonlinear Schrödinger-Korteweg-de Vries equations.  Advances in Nonlinear Analysis.  6:407-426. 2017
  • Ireneo Peral: forty years as mentor.  ADVANCED NONLINEAR STUDIES.  17:217-243. 2017
  • A critical fractional equation with concave convex power nonlinearities.  ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE.  32:875-900. 2015
  • Existence of bound and ground states for a system of coupled nonlinear Schrodinger-KdV equations.  COMPTES RENDUS MATHEMATIQUE.  353:511-516. 2015
  • Existence of solutions for a system of coupled nonlinear stationary bi-harmonic Schrodinger equations.  NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS.  23:78-93. 2015
  • Positive solutions to some systems of coupled nonlinear Schrödinger equations.  NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS.  110:104-112. 2014
  • Perturbations of a critical fractional equation.  PACIFIC JOURNAL OF MATHEMATICS.  271:65-85. 2014
  • Muckenhoupt inequality with three measures and applications to Sobolev orthogonal polynomials.  JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS.  407:369-386. 2013
  • A concave-convex elliptic problem involving the fractional Laplacian.  PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS.  1:39-71. 2013
  • Existence results for some systems of coupled fractional nonlinear Schrodinger equations.  Contemporary Mathematics (Contemporary Mathematics).  595:135-150. 2013
  • Asymptotically Linear Problems and Antimaximum Principle for the Square Root of the Laplacian.  ADVANCED NONLINEAR STUDIES.  12:683-701. 2012
  • On some critical problems for the fractional Laplacian operator.  Journal of Differential Equations.  252:6133-6162. 2012
  • The behavior of the principal eigenvalue of a mixed elliptic problem with respect to a parameter.  JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS.  377:53-69. 2011
  • Multiplicity of Solutions to Uniformly Elliptic Fully Nonlinear Equations with Concave-Convex Right-Hand Side.  Journal of Differential Equations.  246:4221-4248. 2009

• conference contributions 

  • Fractional elliptic problems involving Inverse fractional operators.  353-353. 2019
  • Coupled systems of PDEs related to the fifth state of matter 2018
  • Ground states of some coupled nonlocal fractional dispersive PDEs.  39-53. 2018
  • Results on existence of Vector Bound and Ground state solutions on Systems of coupled NLS and NLS-KdV equations 2017
  • Vector positive solutions for systems of coupled NLS and NLS-KdV equations 2017
  • A mathematical model arising in capillary-gravity water waves.  28-28. 2016
  • Muckenhoupt inequalities with three measures and applications to Sobolev orthogonal polynomials 2016
  • Solutions to some variational PDEs as critical points of their Euler-Lagrange functional.  9-9. 2016
  • Bound and Ground states to systems of coupled NLS-KdV equations 2015
  • Existence and multiplicity of bound-ground states for a system of NLS-KdV equations.  4-4. 2015
  • Existence and multiplicity of solutions for a system of coupled NLS-KdV equations.  92-92. 2015
  • Existence Results for Some Systems of Coupled Fractional Nonlinear Schrodinger Equations 2014
  • Positive Solutions to Some Systems of Coupled Nonlinear Schrodinger Equations 2014
  • A classical critical problem in a non-classical fractional setting 2013
  • Muckenhoupt inequality with three measures and applications to Sobolev Orthogonal Polynomials 2013
  • Elliptic problems involving fractions of the Laplacian operator 2012