Dr. Gilles Evéquoz

Institut für Mathematik
Goethe-Universität Frankfurt
Robert-Mayer-Str. 10
D-60629 Frankfurt
Raum 805


Phone: ++49-69-798-22557
Fax: ++49-69-798-28856
Email: evequoz@math.uni-frankfurt.de

 



Research interests

  • Strongly indefinite problems for PDEs
  • Nonlinear Schrödinger and Helmholtz equations
  • Bifurcation and continuation for ODE and PDE problems
  • Variational and topological methods

 



Teaching

Lectures


Summer term 2014 Analysis 1 (Math BSc + L3, 1st semester)
Winter term 2013/14 Mathematische und statistische Methoden für Pharmazeuten (Pharmacy, 1st semester)
Summer term 2013 Analysis 1 (Math BSc + L3, 1st semester)

Seminars and Exercise sessions (recent)


Summer term 2016 Blockseminar "Integraltransformationen und ihre Anwendungen" with Prof. Dr. Tobias Weth (Math BSc + MSc)
Summer term 2015 Blockseminar "Partielle Differentialgleichungen in Anwendungsbeispielen" with Prof. Dr. Tobias Weth (Math BSc + MSc)
Winter term 2014/15 Exercise session for the course "Ergänzungen zur linearen Funktionalanalysis" (Math BSc + MSc)
Winter term 2014/15 Exercise session for the course "Analysis II" (Math BSc + L3)
Summer term 2014 Blockseminar "Konvexität und Anwendungen" with Prof. Dr. Tobias Weth (Math BSc + MSc)

 



Publications

[15] Multiple standing waves for the nonlinear Helmholtz equation concentrating in the high frequency limit
Annali di Matematica Pura ed Applicata (2017) DOI 10.1007/s10231-017-0651-6, 20 pages ( Preprint )
[14] Existence and asymptotic behavior of standing waves of the nonlinear Helmholtz equation in the plane
Analysis (2017) DOI 10.1515/anly-2016-0023, 14 pages ( Preprint )
[13] (with Tobias Weth) Branch continuation inside the essential spectrum for the nonlinear Schrödinger equation
Journal of Fixed Point Theory and Applications 19 (2017) pp. 475-502 ( Preprint )
[12] On the periodic and asymptotically periodic nonlinear Helmholtz equation
Nonlinear Analysis 152 (2017) pp. 88-101 ( Preprint )
[11] A dual approach in Orlicz spaces for the nonlinear Helmholtz equation
Zeitschrift für angewandte Mathematik und Physik 66 (2015) pp. 2995-3015
[10] (with Tobias Weth) Dual variational methods and nonvanishing for the nonlinear Helmholtz equation
Advances in Mathematics 280 (2015) pp. 690-728 ( Preprint )
[9] (with Tobias Weth) Real solutions to the nonlinear Helmholtz equation with local nonlinearity
Archive for Rational Mechanics and Analysis 211 (2014) pp. 359-388 ( Preprint )
[8] (with Tobias Weth) Entire solutions to nonlinear scalar field equations with indefinite linear part
Advanced Nonlinear Studies 12 (2012) pp. 281-314 ( Preprint )
[7] Parameter-dependent systems on the half-line and free convection boundary-layers in porous media
Nonlinear Differential Equations and Applications 17 (2010) pp. 497-526
[6] Global continuation for first order systems over the half-line involving parameters
Mathematische Nachrichten 282 (2009) pp. 1036-1078. Erratum: 283 (2010) pp. 630-631
[5] (with Charles A. Stuart) Hadamard differentiability and bifurcation
Proceedings of the Royal Society of Edinburgh, Series A 137 (2007) pp. 1249-1285
[4] (with Charles A. Stuart) Bifurcation points of a degenerate elliptic boundary-value problem
Rendiconti dei Lincei, Serie IX Matematica e Applicazioni 17 (2006) pp. 309-334
[3] (with Charles A. Stuart) Bifurcation and concentration of radial solutions of a nonlinear degenerate elliptic eigenvalue problem
Advanced Nonlinear Studies 6 (2006) pp. 215-232
[2] (with Charles A. Stuart) On differentiability and bifurcation
Advances in Mathematical Economics 8 (2006) pp. 155-184
[1] (with Max-Olivier Hongler and Theo Lasser) Resonator stability subject to dynamic random-tilt aberration
Journal of the Optical Society of America A 20 (2003) pp. 151-156