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] "Uncountably many solutions for nonlinear Helmholtz and curl-curl equations", Nov 2018, Advanced Nonlinear Studies. Link

[17] (Accepted) "Bifurcations of nontrivial solutions of a cubic Helmholtz system", with D. Scheider, Nov 2018, to appear in ANONA. Link ArXiv

[16] "On a fourth order nonlinear Helmholtz equation", with D. Bonheure, J.-B. Castéras, Journal of the London Mathematical Society 99 (2019), no. 3, 831-852. Link

[15] "Global secondary bifurcation, symmetry breaking and period-doubling", Topological Methods in Nonlinear Analysis 53 (2019), no.2. Link  

[14] "The limiting absorption principle for periodic differential operators and applications to nonlinear Helmholtz equations", Commun. Math. Phys. 368 (2019), no. 2 799-842. 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, Archive for Rational Mechanics and Analysis 228 (2018), no. 3, 821–866. Link

[11]  "Explicit formulas, symmetry and symmetry breaking for Willmore surfaces of revolution", Annals of Global Analysis and Geometry 54 (2018), no. 2, 187–236. Link

[10] "Oscillating solutions for nonlinear Helmholtz Equations", with E. Montefusco, B. Pellacci,
 Z. Angew. Math. Phys. 68 (2017), no. 6, Art. 121, 19 pp. 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", manuscripta mathematica 154 (2017), no. 3–4, 345–35. 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",  NoDEA Nonlinear Differential Equations Appl. 22 (2015), no. 2, 239–262. Link

[3]  "Uniqueness results for semilinear elliptic systems on R^n",  Math. Nachr. 287 (2014), no. 16, 1828–1836. Link

[2]  "Minimal energy solutions for repulsive nonlinear Schrödinger systems",  J. Differential Equations 257 (2014), no. 2, 450–468. Link

[1]  "Distributional solutions of the stationary nonlinear Schrödinger equation: singularities, regularity and exponential decay", with W.Reichel, Z. Anal. Anwend. 32 (2013), no. 1, 55–82.. Link