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)

[22] (Preprint) "Dispersive estimates, blow-up and failure of Strichartz estimates for the Schrödinger equation with slowly decaying initial data", Oct 2019. Link ArXiv

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

[20] "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, Phys. Rev. A 100, 033819. Link

[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", Adv. Nonlinear Stud. 19 (2019), no. 3, 569–593. Link

[17] "Bifurcations of nontrivial solutions of a cubic Helmholtz system", with D. Scheider, Advances in Nonlinear Analysis, 9(1), 1026–1045. Link

[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, 779–800. 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