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)

[16] (Preprint) "On a fourth order nonlinear Helmholtz equation", with D. Bonheure, J.-B. Castéras, Mar 2018, accepted for publication in JLMS, Link ArXiv

[15] (Preprint) "Global secondary bifurcation, symmetry breaking and period-doubling", Mar 2018, accepted for publication in TMNA, Link ArXiv

[14] (Preprint) "The limiting absorption principle for periodic differential operators and applications to nonlinear Helmholtz equations", Oct 2017, Link ArXiv

[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