Betreute Arbeiten, Publikationen   (Bernhard Lani-Wayda)

                                    
 1.  Betreute Diplom/Bachelor/Master/Staatsexamens-Arbeiten, Dissertationen

 Diplomarbeiten:
 Christian Plitt, Der Fortsetzungssatz von Gaines-Mawhin und die Existenz periodischer Lösungen
                       von periodischen Differentialgleichungen mit zustandsabhängiger Verzögerung. (2007)
Christian Kuhl,  Topologische horseshoes und delay-Differentialgleichungen. (2009)
Carla Terschlüsen,  Symmetrische Funktionaldifferentialgleichungen und neuronale Netze mit Gedächtnis. (2010)

Bachelor theses:
 Robert Zeise,   Flüsse auf dem Torus und die Poincarésche  Rotationszahl.  (2010)
Carsten Mayer,  Numerische Approximation der   Rotationszahl.  (2010)
Silas Maile,  Analyse von numerischen Verfahren zum Lösen  von delay-Differentialgleichungen. (2010)
Paul Sinner,  Stabilitätsuntersuchung von Funktionaldifferentialgleichungen.  (2011)
Katharina Baumann,  Isoperimetrische Ungleichung, Cauchy-Crofton-Formel und inverse Radon-Transformation. (2012)
Björn Gebhard, Topologische Horseshoes, Fixpunktindex und Chaos. (2012)
Lorenzo Ignazio,   Überdeckungseigenschaft für normal hyperbolische Mengen. (2013) 
Marius Scheld,  Lagrange mechanics and geodesic flows. (2013)
Robin Lautenbacher,  Lagrange-Mechanik, Symmetrien und  Kepler-Problem. (2014)
Lukas Rauber, Wesentliche Selbstadjungiertheit und Halbbeschränktheit von Schrödingeroperatoren. (2014)
Felix Hintersehr,  Über Dirac-Operatoren  im Hilbertraum [L^2(R^3)]^4. (2016)
Yannik Hofmann,  Die van der Pol-Differentialgleichung. (2016)
Christian Maximilian Seth,  Über die  Nullstellen transzendenter Funktionen. (2016)
Jasper Clemens Gräflich,  Weierstraß-Darstellung von Minimalflächen. (2016)
Sefa Demirci,  Approximation durch Fourierreihen. (2016)
Laura Momberger, Einführung in Riemannsche Flächen. (2019)
Adrian Bialas, The Nemytskii-Operator on the Two-Dimensional Torus (2024)

Master theses:

Carsten Mayer,   Hyperbolische Mengen und Markov-Partitionen.  (2014)
Paul Sinner,   Die Existenz von Wanderwellen-Lösungen eines diffusiven Räuber-Beute-Systems mit sigmoider Kopplung. (2015)
Philipp Schnecko,  Isolierende Segmente, Fixpunktindex und  symbolische Dynamik.  (2018)
Jasper Clemens Gräflich, Ergodische Zerlegung invarianter Maße. (2019)
Felix Hintersehr, Über Halbflüsse für parabolische partielle Differenzialgleichungen mit zustandsabhängiger Verzögerung. (2019)
Eileen Kaiser, Schwache Lösungen der Navier-Stokes-Gleichungen vom Leray-Hopf-Typ. (2022)
Markus Hindinger, Beispiele geodätischer Flüsse. (2025)

Staatsexamensarbeiten:
David Birk,  Geodätische Flüsse und Hyperbolische Geometrie (2016)
Dennis Horrer,  Analyse der Belousov-Zhabotinsky-Reaktion (2023)

 

Dissertationen:

Vera Ignatenko (Diplom von der Universität St. Petersburg),  Homoclinic solutions for differential equations from physiology.  (2017)
Erkan Muştu (Diplom von der Firat University, Türkei),  Dynamical behavior of a parametrized family of one-dimensional maps.  (2018)

2. Wissenschaftliche Arbeit

Information on current  research interests, as well as abstract or full  text of publications are
available upon request   by e-mail to
Bernhard.Lani-Wayda@math.uni-giessen.de
 

 Publications  since 1992   (Bernhard Lani-Wayda)

[1]  Ivanov, A.,  Lani-Wayda, B. and  Walther, H.O.:
 Unstable hyperbolic  periodic solutions of differential delay equations.
In: Recent Trends in Differential Equations, ed. R.P. Agarwal, 301-316,
World Scientific, Singapore 1992.

[2] Lani-Wayda, B.:  Hyperbolic Sets, Shadowing and Persistence for Noninvertible
Mappings in  Banach Spaces.  Pitman Research Note in Mathematics No. 334,
Longman Group Ltd,  Harlow, Essex, 1995 (144 pages).

[3]  Lani-Wayda, B.:  Persistence of Poincaré mappings in functional differential
equations (with application to structural stability  of complicated behavior).
  J.  Dynam.  Differential  Equations  Vol.  7, No. 1  (1995), 1-71.
(Featured review MR 96 e:34118.)

[4] Dormayer, P. and Lani-Wayda, B.:  Floquet multipliers and
 Secondary Bifurcations in Functional Differential Equations.
 Numerical and Analytical Results.
Z. Angew. Math. Phys. (ZAMP)   46 (1995), 823-858.

[5] Lani-Wayda, B. and Walther, H.-O.: Chaotic motion generated
by negative delayed feedback. Part I: A transversality criterion.
Differential Integral Equations  Vol.  8, No. 6 (1995), 1407-1452.

[6] Lani-Wayda, B. and  Walther, H.-O.: Chaotic motion generated
  by delayed negative feedback, Part II: Construction of nonlinearities.
 Math.  Nachr.   180 (1996), 141-211.

[7] Lani-Wayda, B.: Erratic solutions of  simple delay equations,
Trans.  Amer. Math. Soc.  351  (1999), 901-945.

[8] Lani-Wayda, B.: Equivalence of the Euler equation with a variational problem.
J. Math. Fluid Mech.  1  (1999), 388-408.

[9] Lani-Wayda, B.: Wandering solutions of delay equations with sine-like feedback.
Mem. Amer. Math. Soc. Vol. 151, No. 718 (2001), American Mathematical Society,
Providence, RI (120 pages).

[10] Lani-Wayda, B.: Representing Poincaré maps by return times. In:
Differential Equations and Dynamical Systems, A. Galves, J.K. Hale, C. Rocha (eds.),
Fields Institute Communications 31 (2002), 217-233, American Mathematical Society, Providence, RI.

[11] Dormayer, P., Ivanov, A.F., and  Lani-Wayda, B.:   Floquet multipliers  of rapidly
oscillating periodic solutions of delay equations.
Tohoku Math. J. 54   (2002), 419-441.  

[12]  Lani-Wayda, B., und Srzednicki, R.:  The Lefschetz fixed
point theorem and symbolic dynamics in delay equations. 
Ergodic Theory and Dynam.  Systems 22  (2002), 1215-1232.

[13]  Ivanov, A.F., and  Lani-Wayda, B.:  Periodic solutions for three-dimensional systems   with time delays. 
Discrete Contin. Dyn. Syst. Vol. 11,  No. 2,3 (2004), 667-692.

[14]  Lani-Wayda, B., and Schneider, K.:  Delayed  loss of
stability in differential equations with retarded argument.
  SIAM J. Math.  Anal.  36,  No. 5 (2005), 1522-1539.

[15]  Ivanov, A.F. , and Lani-Wayda, B.:  Stability and instability
criteria for Kaplan-Yorke solutions.  Z. angew. Math. Phys. 57  (2006),  1-29.

[16]  Lani-Wayda,  B.:  Change of the attractor structure for  x'(t) = f(x(t-1))
 when f changes from monotone to  non-monotone negative feedback. J. Differential Equations Vol. 248  No. 5, (2010),
1120-1142.  https://doi.org/10.1016/j.jde.2009.11.016 

[17]  Lani-Wayda, B.:  Hopf Bifurcation for Retarded Functional Differential Equations and for Semiflows in Banach Spaces.
J.  Dynam.  Differential Equations Vol. 25, No. 4 (2013), 1159-1199.
https://doi.org/10.1007/s10884-013-9334-1 

[18] Lani-Wayda, B.,  and Walther, H.-O.: A Shilnikov phenomenon due to state-dependent delay, by means of the fixed point index.
J.  Dynam.  Differential Equations  Vol. 28 No. 3 (2016), 627-688. https://doi.org/10.1007/s10884-014-9420-z

[19]  Burkhardt, S.,  M.T. Elm,  P.J.  Klar (JLU Gießen, Materialwissenschaft bzw. Chemie),   und Lani-Wayda, B.:
 In Situ Monitoring of Lateral Hydrogen Diffusion in Amorphous and Polycrystalline WO3 Thin Films, Advanced Materials Interfaces 2018.
   http://onlinelibrary.wiley.com/doi/10.1002/admi.201701587/pdf 

[20]  Ivanov, A.F., and Lani-Wayda, B.: Periodic solutions for an N-dimensional cyclic feedback system with delay,
 J. Differential Equations,  Vol. 268 No.  9 (2020),  5366-5412.   https://doi.org/10.1016/j.jde.2019.11.028 

[21]  Ivanov, A.F., and Lani-Wayda, B.: Periodic Solutions in a Differential Delay
Equation Modeling Megakaryopoiesis. In:  Analysis, Applications and Computation, Proceedings of the 13th ISAAC congress (2021),(pp. 89-100), 
Birkhäuser 2023, Springer `Trends in Mathematics' book series,  https://doi.org/10.1007/978-3-031-36375-7_4 

[22] Lani-Wayda, B. and Godoy Mesquita, J.: Linearized instability for differential equations with dependence on the past derivative. Electron. J. Qual. Theory Differ. Equ. 2023, Paper No. 52. 
https://doi.org/10.14232/ejqtde.2023.1.52

 

Work  submitted in 2024: 

[23]  Ivanov, A. F.,  Lani-Wayda, B. and Shelyag. S. (Flinders University, Adelaide, Australia): Periodic Solutions of a Delay Differential Equation with a Periodic Multiplier.

[24]  Ivanov, A., and  Lani-Wayda, B.:  The strong  unstable manifold and periodic solutions in  differential delay  equations with cyclic monotone negative feedback.