Research
Fields of interest: I am interested in Nonlinear Elliptic Partial Differential Equations that appear in Mathematical Physics and Geometry. In my work the main tools for this study are variational methods, topological methods, and perturbation arguments. For instance, I have worked on the Stationary Nonlinear
Schrödinger Equation (and other models alike) and the existence of semiclassical states. Moreover, I am involved in the application of variational methods to Liouvilletype equations on compact surfaces that appear in ChernSimons theory and Geometrical Analysis. More recently I am also working on semilinear elliptic problems under overdetermined boundary conditions.
Here you can find a short CV. For a complete list of publications see below.
Some slides: The following slides give a good idea of my recent work and my current interests:

In 2015 I gave a conference at the "Equadiff" held in Lyon (France).

In 2017 I gave a conference at the 1st Belgium+Italy+Chile Conference in PDE’s held in Brussels (Belgium).

In 2018 I gave a conference at the ICM Satellite Conference in Nonlinear PDE, Fortaleza (Brasil).

In 2020 I gave a conference at the online seminar "PDEs: España vs Italia".
For any question, doubt or comment, please do not hesitate and contact me at
the address daruiz hat ugr.es.
Editorial work:
Articles:

Sergio CruzBlázquez, Andrea Malchiodi and David Ruiz, Conformal metrics with prescribed scalar and mean curvature, preprint arXiv.org/pdf/2105.04185.pdf

Jacopo Bellazzini and David Ruiz, Finite energy travelling waves for the GrossPitaevskii equation in the subsonic regime, preprint arXiv.org/pdf/1911.02820.

Aleks Jevnikar, Rafael López Soriano, María Medina and David Ruiz, Blowup analysis of conformal metrics of the disk with prescribed Gaussian and geodesic curvatures, preprint arXiv.org/pdf/2004.14680, to appear in Analysis and PDEs.

R. LópezSoriano, A. Malchiodi and D. Ruiz, Conformal metrics with prescribed Gaussian and geodesic curvatures, preprint arXiv.org/abs/1806.11533, to appear in Ann. Sci. de l'École Normale Supérieure.

A. Ros, D. Ruiz and P. Sicbaldi, "Solutions to overdetermined elliptic problems in nontrivial exterior domains", J. European Math. Society 22 (2020), 253281.

S. CruzBlázquez and D. Ruiz, "Prescribing Gaussian and geodesic curvature on the disk", Advanced Nonlinear Studies 18 (2018), 453468.

D. Ruiz and J. Van Schaftingen, "Odd symmetry of least energy nodal solutions for the Choquard equation", J. Differential Equations 264 (2018), 12311262.

F. De Marchis, R. LópezSoriano and D. Ruiz, "Compactness, existence and multiplicity for the singular mean field problem with signchanging potentials", J. Math. Pures Appliquées 115 (2018), 237267.

A. Ros, D. Ruiz and P. Sicbaldi, "A rigidity result for overdetermined elliptic problems in the plane" , Comm. Pure Appl. Math. 70 (2017), 12231252.

T. D'Aprile, A. Pistoia and D. Ruiz, "Asymmetric blowup for the SU(3) Toda System", J. Funct. Anal. 271 (2016), 495531.

Y. Jiang, A. Pomponio and D. Ruiz, "Standing waves for a gauged nonlinear Schrödinger equation with a vortex point", Comm. Contemp. Math 18 (2016), 1550074 (20 pages).

R. LópezSoriano and D. Ruiz, "Prescribing the Gaussian curvature in a subdomain of S^2 with Neumann boundary condition", J. Geom. Anal. 26 (2016), 630–644.

T. D'Aprile, A. Pistoia and D. Ruiz, "A continuum of solutions for the SU(3) Toda System exhibiting partial blowup", Proc. London Math. Soc. 111 (2015), 797830.

L. Battaglia, A. Jevnikar, A. Malchiodi and D. Ruiz, "A general existence result for the Toda system on compact surfaces", Advances in Mathematics 285 (2015), 937979.

A. Malchiodi and D. Ruiz, "On the LeraySchauder degree of the Toda system on compact surfaces", Proc. AMS. 143 (2015), 2985–2990.

A. Pomponio and D. Ruiz, "Boundary concentration of a Gauged Nonlinear Schrodinger Equation", Calc. Var. PDE 53 (2015), 289316

A. Pomponio and D. Ruiz, "A Variational Analysis of a Gauged Nonlinear Schrödinger Equation", J. Eur. Math. Soc 17 (2015), 14631486.

A. Malchiodi and D. Ruiz, “A variational Analysis of the Toda System on Compact Surfaces”, Comm. Pure Appl. Math. 66 (2013), 332371.

D. Ruiz, "A note on the uniformity of the constant in the Poincaré
inequality", special volume dedicated to A. Ambrosetti, Advanced Nonlinear Studies 12 (2012), 889903.

P. D'Avenia, A. Pomponio and D. Ruiz, “Semiclassical states for the Nonlinear Schrödinger Equation on saddle points of the potential via variational methods ”, Journal of Functional Analysis, 262 (2012), 46004633.

I. Ianni y D. Ruiz, “Ground and bound states for a static SchrodingerPoissonSlater problem”, Comm. Contemp. Mathematics 14, (2012), No. 1.

A. Malchiodi and D. Ruiz, “New improved MoserTrudinger inequalities and singular Liouville equations on compact surfaces”, GAFA 21 (2011), 11961217.

T. D’Aprile and D. Ruiz, “Positive and signchanging clusters around saddle points of the potential for nonlinear elliptic problems”, Mathematische Zeitschrift 268 (2011), 605634.

D. Ruiz y G. Vaira, “Cluster solutions for the SchrödingerPoissonSlater problem around a local minimum of the potential”, Revista Matemática Iberoamericana 27 (2011), 253271.

D. Ruiz, “On the SchrödingerPoissonSlater system: behavior of minimizers, radial and nonradial cases”, Archive for Rational Mechanics and Analysis 198 (2010), 349368.

D. Ruiz and G. Siciliano, “Existence of ground states for a modified nonlinear Schrodinger equation”, Nonlinearity 23 (2010), 12211233.

A. Ambrosetti and D. Ruiz , “Multiple bound states for the SchrödingerPoisson problem”, Comm. Contemp. Math. 10 (2008), 391404.

A. Ambrosetti, G. Cerami and D. Ruiz, “Solitons of linearly coupled systems of semilinear nonautonomous equations on R^N” , Journal of Functional Analysis 254 (2008), 28162845.

D. Ruiz and G. Siciliano, “A note on the SchrödingerPoissonSlater equation on bounded domains” , Advanced Nonlinear Studies 8 (2008), 179190.

D. Ruiz and A. Suárez, “Existence and uniqueness of positive solution of a logistic equation with nonlinear gradient term”, Proc. Royal Soc. Edinburgh Sect. A 137 (2007), 555566.

A. Ambrosetti, E. Colorado and D. Ruiz, “Multibump solitons to linearly coupled systems of nonlinear Schrödinger equations”, Calculus of Variations and PDE 30 (2007), 85112.

D. Ruiz, “ The SchrödingerPoisson equation under the effect of a nonlinear local term”, Journal of Functional Analysis 237 (2006), 655674.

A. Ambrosetti and D. Ruiz, “ Radial solutions concentrating on spheres of Nonlinear Schrödinger equations with vanishing potentials” , Proc. Royal Soc. Edinburgh 136 A (2006), 889907.

D. Arcoya and D. Ruiz, “The AmbrosettiProdi problem for the plaplace operator”, Comm. in PDE 31 (2006), 849865.

A. Ambrosetti, A. Malchiodi and D. Ruiz, “ Bound states of nonlinear Schrödinger equations with potentials vanishing at infinity”, Journal d'Analyse Mathématique 98 (2006), 317348.

A. Cañada and D. Ruiz, “ Asymptotic analysis of oscillating parametric integrals and ordinary boundary value problems at resonance”, Journal of Math. Anal. and Appl. 313 (2006), 218233.

D. Ruiz, “ Semiclassical states for coupled SchrödingerMaxwell equations: concentration around a sphere”, Mathematical Models and Methods in Applied Sciences 15 (2005), 141164.

A. Ambrosetti, A. Malchiodi and D. Ruiz, "Recent trends on nonlinear elliptic equations on $R^n$" . Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. (5) 29 (2005), 3–13.

A. Cañada and D. Ruiz, “ Periodic perturbations of a class of resonant problems”, Calculus of Variations and PDE 23 (2005), 281300.

D. Ruiz and J. R. Ward, “ Some notes on periodic systems with linear part at resonance”, Discrete and Continuous Dynamical Systems 11 (2004), 337350.

D. Ruiz, “ A priori estimates and existence of positive solutions for strongly nonlinear problems” , Journal of Diff. Eq. 199 (2004), 96114.

D. Ruiz, “ Resonant semilinear problems with nonlinear term depending on the derivative” , Journal of Math. Analysis and Appl. 295 (2004), 163173.

D. Bonheure, C. Fabry and D. Ruiz, “ Problems at resonance for equations with periodic nonlinearities ”, Nonlinear Analysis 55 (2003), no. 5, 557581.

D. Ruiz and M. Willem, “ Elliptic problems with critical exponent and Hardy potentials ”, Journal of Diff. Eq. 190 (2003), 524538.

J. Mawhin and D. Ruiz, “ A strongly nonlinear Neumann problem at resonance with restrictions on the nonlinearity just in one direction ”, Topol. Meth. in Nonl. Anal. 20 (2002), 114.

A. Cañada and D. Ruiz, “ Resonant problems with multidimensional kernel and periodic nonlinearities ”, Diff. Int. Equations 16 (2003), 499512.

A. Cañada and D. Ruiz, “ Resonant nonlinear boundary value problems with almost periodic nonlinearity ”, B. Belgian. Math. Soc.Simon Stevin 9 (2002), 193204.