Main research topics and interests:

  • Nonlinear Helmholtz Equations
  • Nonlinear Schrödinger Equations
  • Calculus of Variations
  • Bifurcation Theory

 

Publications and Preprints   (listed according to the submission date)

[21] (Preprint) "On Helmholtz equations and counterexamples to Strichartz estimates in hyperbolic space", with J.-B. Casteras, Feb 2019 Link ArXiv

[20] (Preprint) "Bandwidth and conversion efficiency analysis of dissipative Kerr soliton frequency combs based on bifurcation theory", with J. Gärtner, P. Trocha, C. Koos, T. Jahnke, W. Reichel, Dec 2018, Link CRC 1173 "Wave phenomena" preprints

[19] (Preprint) "The Lugiato-Lefever equation with nonlinear damping caused by two photon absorption", Nov 2018, Link ArXiv

[18] (Preprint) "Uncountably many solutions for nonlinear Helmholtz and curl-curl equations with general nonlinearities", Nov 2018, Link ArXiv.

[17] (Preprint) "Bifurcations of nontrivial solutions of a cubic Helmholtz system", with D. Scheider, Nov 2018, Link ArXiv

[16] (Accepted) "On a fourth order nonlinear Helmholtz equation", with D. Bonheure, J.-B. Castéras, Mar 2018, to appear in JLMS, Link

[15] (Accepted) "Global secondary bifurcation, symmetry breaking and period-doubling", Mar 2018, to appear in TMNA, Link ArXiv

[14] (Accepted) "The limiting absorption principle for periodic differential operators and applications to nonlinear Helmholtz equations", Oct 2017, to appear in Communications in Mathematical Physics Link

[13] "Dual variational methods for nonlinear Helmholtz systems", with D.Scheider, NoDEA Nonlinear Differential Equations Appl. 25 (2018), no. 2, 25:13. Link

[12] "Periodic Solutions to a Cahn–Hilliard–Willmore Equation in the Plane", with A. Malchiodi, M. Rizzi, Arch Rational Mech Anal (2017). Link

[11]  "Explicit formulas, symmetry and symmetry breaking for Willmore surfaces of revolution", Mandel, R. Ann Glob Anal Geom (2018). Link

[10] "Oscillating solutions for nonlinear Helmholtz Equations", with E. Montefusco, B. Pellacci,
Z. Angew. Math. Phys. 68 (2017), no. 6, 68:121. Link

[9]  "A priori bounds and global bifurcation results for frequency combs modeled by the Lugiato-Lefever equation", with W. Reichel, SIAM J. Appl. Math. 77 (2017), no. 1, 315–345. Link

[8] "A note on the local regularity of distributional solutions and subsolutions", Sep 2015. Link

[7] "Minimal energy solutions and infinitely many bifurcating branches for a class of saturated nonlinear Schrödinger systems", Adv. Nonlinear Stud. 16 (2016), no. 1, 95–113. Link

[6]  "Boundary value problems for Willmore curves in R^2", Calc. Var. Partial Differential Equations 54 (2015), no. 4, 3905--3925. Link

[5]  "Infinitely many global continua bifurcating from a single solution of an elliptic problem with concave-convex nonlinearity", with T. Bartsch, J. Math. Anal. Appl. 433 (2016), no. 2, 1006--1036. Link

[4]  "Minimal energy solutions for cooperative nonlinear Schrödinger systems", Feb 2014, published in NoDEA, volume 22 (2015), number 2, pp. 239--262. Link

[3]  "Uniqueness results for semilinear elliptic systems on R^n", May 2013, published in    Mathematische Nachrichten, volume 287 (2014), issue 16, pp. 1828–-1836. Link

[2]  "Minimal energy solutions for repulsive nonlinear Schrödinger systems", Mar 2013, published in the Journal of Differential Equations, volume 257 (2014), number 2, pp. 450--468. Link

[1]  "Distributional solutions of the stationary nonlinear Schrödinger equation: singularities, regularity and exponential decay", with W.Reichel, Oct 2011, published in ZAA. Link