# Dr. François Genoud

## Director

Cours de Mathématiques Spéciales

Ecole Polytechnique Fédérale de Lausanne
Office BS 282 (BS Building)
1015 Lausanne, Switzerland

francois.genoud@epfl.ch
+41 21 693 22 91

### Short vita:

2018-        : Director, CMS

2017-2018: Associate Professor at the Université Libre de Bruxelles

2015-2017: Assistant Professor at the Delft University of Technology

2013-2015: Postdoc at the University of Vienna

2010-2013: Postdoc at Heriot-Watt University (Edinburgh)

2009-2010: Postdoc at the University of Oxford

2005-2008: Graduate studies in Mathematics at EPFL

2000-2005: Undergraduate studies in Physics at EPFL

Here is an extended version: CV

### Research interests:

Partial differential equations, evolution equations, nonlinear analysis, bifurcation theory, calculus of variations, mathematical physics.

### Publications:

27. (with E. Csobo) Minimal mass blow-up solutions for the $L^2$ critical NLS with inverse-square potential, Nonlinear Anal. 168 (2018), 110-129, arXiv_1707.01421.

26. Instability of an integrable nonlocal NLS, C. R. Math. Acad. Sci. Paris 355 (2017), 299-303, arXiv_1612.03139.

25. Extrema of the dynamic pressure in a solitary wave, Nonlinear Anal. 155 (2017), 65-71, arXiv_1612.07918.

24. (with S. Bachmann) Mean-field limit and phase transitions for nematic liquid crystals in the continuum, J. Stat. Phys. 168 (2017), 746-771, arXiv_1508.05025.

23. (with V. Combet) Classification of minimal mass blow-up solutions for an $L^2$ critical inhomogeneous NLS, J. Evol. Equ. 16 (2016), 483-500, arXiv_1503.08915.

22. (with B. A. Malomed and R. M. Weishäupl) Stable NLS solitons in a cubic-quintic medium with a delta-function potential, Nonlinear Anal. 133 (2016), 28-50, arXiv_1409.6511.

21. (with S. de Bièvre and S. Rota Nodari) Orbital stability: analysis meets geometry, in: C. Besse, J. C. Garreau (eds.), Nonlinear Optical and Atomic Systems, Lecture Notes in Mathematics 2146, Springer, 2015, pp. 147-273, ISBN 978-3-319-19015-0, arXiv_1407.5951.

20. (with A. Derlet) Existence of nodal solutions for quasilinear elliptic problems in $R^N$, Proc. Roy. Soc. Edinburgh Sect. A 145 (2015), 937-957, arXiv_1312.3457.

19. (with D. Henry) Instability of equatorial water waves with an underlying current, J. Math. Fluid Mech. 16 (2014), 661-667, arXiv_1403.1880.

18. Monotonicity of bifurcating branches for the radial p-Laplacian, Monografías Matemáticas García de Galdeano 39 (2014), 111-119.

17. Some bifurcation results for quasilinear Dirichlet boundary value problems, Electron. J. Diff. Equ. Conference 21 (2014), 87-100.

16. Orbitally stable standing waves for the asymptotically linear one-dimensional NLS, Evolution Equations and Control Theory 2 (2013), 81-100, arXiv_1209.2057.

15. (with B. P. Rynne) Landesman-Lazer conditions at half-eigenvalues of the p-Laplacian, J. Differential Equations 254 (2013), 3461-3475, arXiv_1207.2489.

14. Global bifurcation for asymptotically linear Schrödinger equations, NoDEA Nonlinear Differential Equations Appl. 20 (2013), 23-35, arXiv_1106.5879.

13. Bifurcation along curves for the p-Laplacian with radial symmetry, Electron. J. Diff. Equ. 2012, no. 124, arXiv_1202.4654.

12. (with B. P. Rynne) Half eigenvalues and the Fucik spectrum of multi-point, boundary value problems, J. Differential Equations 252 (2012), 5076-5095, arXiv_1110.0712.

11. An inhomogeneous, $L^2$ critical, nonlinear Schrödinger equation, Z. Anal. Anwend. 31 (2012), 283-290, arXiv_1110.0915.

10. (with B. P. Rynne) Some recent results on the spectrum of multi-point eigenvalue problems for the p-Laplacian, Commun. Appl. Anal. 15 (2011), 413-434.

9. Bifurcation from infinity for an asymptotically linear problem on the half-line, Nonlinear Anal. 74 (2011), 4533-4543.

8. (with B. P. Rynne) Second order, multi-point problems with variable coefficients, Nonlinear Anal. 74 (2011), 7269-7284, arXiv_1106.3936.

7. Nonlinear Schrödinger equations on $R$: global bifurcation, orbital stability and nonlinear waveguides, Commun. Appl. Anal. 15 (2011), 395-412.

6. A uniqueness result for $\Delta u – \lambda u + V(|x|) u^p = 0$ on $R^2$, Adv. Nonlinear Stud. 11 (2011), 483-491.

5. A smooth global branch of solutions for a semilinear elliptic equation on $R^N$, Calc. Var. Partial Differential Equations 38 (2010), 207-232.

4. Bifurcation and stability of travelling waves in self-focusing planar waveguides, Adv. Nonlinear Stud. 10 (2010), 357-400.

3. Existence and orbital stability of standing waves for some nonlinear Schrödinger equations, perturbation of a model case, J. Differential Equations 246 (2009), 1921-1943.

2. Existence and stability of high frequency standing waves for a nonlinear Schrödinger equation, Discrete Contin. Dyn. Syst. 25 (2009), 1229-1247.

1. (with C. A. Stuart) Schrödinger equations with a spatially decaying nonlinearity: existence and stability of standing waves, Discrete Contin. Dyn. Syst. 21 (2008),137-186.

Last updated September 18, 2018.