99.
mit D. E. Pelinovsky: Dynamics of the black soliton in a regularized nonlinear Schrödinger equation. Proceedings of the American Mathematical Society 152 (3), 1217-1231 (2024). https://doi.org/10.1090/proc/16633

98.
mit R. Venkitakrishnan, Y. Augenstein, B. Zerulla, F. Z. Goffi und C. Rockstuhl: On the Physical Significance of Non-Local Material Parameters in Optical Metamaterials. New Journal of Physics 25 123014. https://iopscience.iop.org/article/10.1088/1367-2630/ad1010

97.
mit X. Liao: Eigenvalue analysis of the Lax operator for the one-dimensional cubic nonlinear defocusing Schrödinger equation. SIAM Journal on Mathematical Analysis 55 (6), 7399-7425 (2023). https://doi.org/10.1137/23M1550232

96.
mit W. Reichel: Breathers and Rogue Waves for Semilinear curl-curl Wave Equations. Journal of Elliptic and Parabolic Equations 9, 757-780 (2023). https://doi.org/10.1007/s41808-023-00215-x

95.
mit D. E. Pelinovsky: Stability of black solitons in optical systems with intensity-dependent dispersion. SIAM Journal on Mathematical Analysis 56 (2), 2521-2568 (2024). https://doi.org/10.1137/23M1552838 ; arXiv 2022. https://doi.org/10.48550/arXiv.2205.10177

94.
mit B. M. Brown, T. Dohnal und I. Wood: Spectrum of the Maxwell Equations for a Flat Interface between Homogeneous Dispersive Media. Communications in Mathematical Physics 406, 3 (2025). https://doi.org/10.1007/s00220-024-05154-9

93.
mit A. Khrabustovskyi: Operator estimates for homogenization of the Robin Laplacian in a perforated domain. Journal of Differential Equations 338, 474-517 (2022). https://doi.org/10.1016/j.jde.2022.08.005

92.
mit F. Z. Goffi, A. Khrabustovskyi, R. Venkitakrishnan und C. Rockstuhl: Higher order constitutive relations and interface conditions for metamaterials with strong spatial dispersion. Physics Letters A 412, 127570 (2021). https://doi.org/10.1016/j.physleta.2021.127570

91.
mit K. Tanaka, K. Sekine, M. Kashiwagi und S. Oishi: Rigorous numerical enclosures for positive solutions of Lane-Emden's equation with sub-square exponents. Numerical Functional Analysis and Optimization 43 (3), 322-349 (2022). https://www.tandfonline.com/doi/full/10.1080/01630563.2022.2029485 ; http://arxiv.org/abs/1607.04619

90.
mit B. Fazekas und F. Pacella: Approximate nonradial solutions for the Lane-Emden problem in the ball. Adv. Nonlinear Anal. 11, 268-284 (2022). https://doi.org/10.1515/anona-2020-0191

89.
mit R. Venkitakrishnan, T. Höß, T. Repän, F. Z. Goffi und C. Rockstuhl: Lower limits for the homogenization of periodic metamaterials made from electric dipolar scatterers. Physical Review B 103, 195425 (2021). https://doi.org/10.1103/PhysRevB.103.195425

88.
mit G. Alefeld und Ch. Wieners: Error bounds and enclosures: The development of numerical analysis and the impact of the contributions by Lothar Collatz. ZAMM 100, 1-8 (2020). https://doi.org/10.1002/zamm.202002042

87.
mit J. Wunderlich: Computer-assisted Existence Proofs for One-dimensional Schrödinger-Poisson Systems. Acta Cybernetica 24, 373-391 (2020). https://doi.org/10.14232/actacyb.24.3.2020.6

86.
mit M. T. Nakao und Y. Watanabe: Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations. Springer Series in Computational Mathematics 53, Springer Singapore, 2019. https://doi.org/10.1007/978-981-13-7669-6

85.
mit F. Z. Goffi, K. Mnasri, C. Rockstuhl und A. Khrabustovskyi: Towards more general constitutive relations for metamaterials: A checklist for consistent formulations. Phys. Rev. B 101, 195411 (2020). https://doi.org/10.1103/PhysRevB.101.195411

84.
mit K. Nagatou und P. J. McKenna: Orbital stability investigations for travelling waves in a nonlinearly supported beam. Journal of Differential Equations 268 (1), 80-114 (2019).https://doi.org/10.1016/j.jde.2019.08.008

83.
mit B. M. Brown, V. Hoang, M. Radosz und I. Wood: Gap localization of TE-modes by arbitrarily weak defects - multiband case. J. London Math. Soc. (2) 00, 1-23 (2020). https://doi.org/10.1112/jlms.12337

82.
mit K. Mnasri, F. Goffi und C. Rockstuhl: Homogenization of wire media with a general purpose nonlocal constitutive relation. J. Opt. Soc. Am. B 36 (8), pp. F99-F108 (2019). https://doi.org/10.1364/JOSAB.36.000F99

81.
mit K. Mnasri, A. Khrabustovskyi und C. Rockstuhl: Retrieving effective material parameters of metamaterials characterized by nonlocal constitutive relations. Phys. Rev. B 99 (3), 035442 (2019). https://doi.org/10.1103/PhysRevB.99.035442

80.
mit J. Feis, K. Mnasri, A. Khrabustovskyi, Ch. Stohrer und C. Rockstuhl: Surface plasmon polaritons sustained at the interface of a nonlocal metamaterial. Phys. Rev. B 98, 115409 (2018). https://journals.aps.org/prb/abstract/10.1103/PhysRevB.98.115409

79.
mit A. Khrabustovskyi, K. Mnasri, Ch. Stohrer und C. Rockstuhl: Beyond local effective material properties for metamaterials. Phys. Rev. B 97, 075439 (2018). https://doi.org/10.1103/PhysRevB.97.075439

78.
mit A. Khrabustovskyi, K. Mnasri, Ch. Stohrer und C. Rockstuhl: Interface conditions for a metamaterial with strong spatial dispersion. http://arxiv.org/abs/1710.03676

77.
mit A. Khrabustovskyi, K. Mnasri, Ch. Stohrer und C. Rockstuhl: Beyond local effective material properties for metamaterials. http://arxiv.org/abs/1705.10969v1

76.
mit A. Contreras und D. E. Pelinovsky: Orbital Stability of Domain Walls in Coupled Gross-Pitaevskii Systems. SIAM J. Math. Anal. 50, No. 1, 810-833 (2018). doi: 10.1137/17M1114892. http://arxiv.org/abs/1702.00701

75.
mit W. Reichel: A breather construction for a semilinear curl-curl wave equation with radially symmetric coefficients. W. J. Elliptic Parabol. Equ. 2, 371-387 (2016). https://doi.org/10.1007/BF03377410

74.
mit A. Khrabustovskyi: Spectral properties of elliptic operators with double-contrast coefficients near a hyperplane. Asymptotic Analysis 98, 91-130 (2016). https://doi.org/10.3233/ASY-161363

73.
mit B. M. Brown, V. Hoang, M. Radosz und I. Wood: Gap localization of TE-Modes by arbitrarily weak defects. Journal of the London Mathematical Society (2) 95, no. 3, 942-962 (2017). https://doi.org/10.1112/jlms.12046

72.
mit Y. Watanabe, K. Nagatou und M. T. Nakao: Norm bound computation for inverses of linear operators in Hilbert spaces. Journal of Differential Equations 260, 6363-6374 (2016). https://doi.org/10.1016/j.jde.2015.12.041

71.
mit F. Pacella und D. Rütters: A computer-assisted existence proof for Emden's equation on an unbounded L-shaped domain. Communications in Contemporary Mathematics, Vol. 19, No. 2 (2017). http://doi.org/10.1142/S0219199717500055

70.
mit Th. Bartsch, T. Dohnal und W. Reichel: Ground states of a nonlinear curl-curl problem in cylindrically symmetric media. Nonlinear Differ. Equ. Appl. (2016) 23: 52. https://doi.org/10.1007/s00030-016-0403-0

69.
mit B. M. Brown, V. Hoang und I. Wood: Spectrum created by line defects in
periodic structures. Mathematische Nachrichten 287, Nr. 17-18, 1972-1985. https://doi.org/10.1002/mana.201300165

68.
mit Y. Watanabe, K. Nagatou und M. T. Nakao: Verified Computations of Eigenvalue Exclosures for Eigenvalue Problems in Hilbert Spaces. SIAM J. Numer. Anal., Vol. 52, No. 2, 975-992, 2014. https://doi.org/10.1137/120894683

67.
mit P. J. McKenna, F. Pacella und D. Roth: A Computer-Assisted Uniqueness Proof for a Semilinear Elliptic Boundary Value Problem. Inequalities and Applications 2010, International Series of Numerical Mathematics, Vol. 161, Part 1, 31-52, 2012. Artikel

66.
mit C. Bandle, A. Gilanyi und L. Losonczi: Inequalities and Applications 2010 (Dedicated to the Memory of Wolfgang Walter), International Series of Numerical Mathematics, Vol. 161, Springer Basel, 2012. Buch

65.
mit B. M. Brown, V. Hoang und I. Wood: On the spectrum of waveguides in planar photonic bandgap structures. Proceedings of the Royal Society of London A, 471: 20140673, http://dx.doi.org/10.1098/rspa.2014.0673

64.
mit T. Dohnal, K. Nagatou und W. Reichel: Interfaces supporting surface gap soliton ground states in the 1D nonlinear Schrödinger equation. Journal of Mathematical Analysis and Applications 407 (2013), pp. 425-435. http://doi.org/10.1016/j.jmaa.2013.05.028

63.
mit K. Nagatou, M. T. Nakao und Y. Watanabe: A computer-assisted stability proof for the Orr-Sommerfeld problem with Poiseuille flow. Nonlinear Theory and Its Applications, IEICE 2, 123-127 (2011).

62.
mit K. Nagatou und M. T. Nakao: Eigenvalue excluding for perturbed-periodic one-dimensional Schrödinger operators. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 468, Issue 2138 (2012), pp. 545-562. http://doi.org/10.1098/rspa.2011.0159 pdf

61.
mit T. Dohnal und W. Reichel: Surface gap soliton ground states for the nonlinear Schrödinger equation. Comm. Math. Phys., Volume 308, Issue 2 (2011), 511-542; https://link.springer.com/article/10.1007/s00220-011-1320-z pdf

60.
mit W. Dörfler, A. Lechleiter, G. Schneider und Ch. Wieners: Photonic Crystals: Mathematical Analysis and Numerical Approximation. Birkhäuser, 2010; Oberwolfach Seminars 42.

59.
mit T. Dohnal und W. Reichel: Localized modes of the linear periodic Schrödinger operator with a nonlocal perturbation. SIAM J. Math. Anal., Volume 41, Issue 5 (2009), 1967-1993. pdf

58.
mit B. M. Brown, V. Hoang und I. G. Wood: Floquet-Bloch Theory for Elliptic Problems with Discontinuous Coefficients. In: Spectral theory and analysis, 1–20, Oper. Theory Adv. Appl., 214, Birkhäuser/Springer, Basel, 2011.

57.
mit P. J. McKenna, F. Pacella und D. Roth: A Uniqueness Result for a Semilinear Elliptic Problem: A Computer-assisted Proof. J. Differential Equations 247 (2009) 2140-2162; http://doi.org/10.1016/j.jde.2009.06.023

56.
Computer-assisted Proofs for Semilinear Elliptic Boundary Value Problems. Japan Journal for Industrial and Applied Mathematics, Vol. 26, No. 2-3 (2009); http://doi.org/10.1007/BF03186542

55.
mit V. Hoang und Ch. Wieners: A computer-assisted proof for photonic band gaps. Z. angew. Math. Phys. 60 (2009) 1035-1052; 0044-2275/09/061035-18; http://doi.org/10.1007/s00033-008-8021-2

54.
mit B. M. Brown, V. Hoang und I.G. Wood: On Spectral Bounds for Photonic Crystal Waveguides. In: Inequalities and Applications (C. Bandle, A. Gilànyi, L. Losonczi, Z. Pales, M. Plum eds.), International Series of Numerical Mathematics, Vol. 157, 23-30 (2009).

53.
mit Y. Watanabe und M. T. Nakao: A computer-assisted instability proof for the Orr-Sommerfeld problem with Poiseuille flow. Z. Angew. Math. Mech. 89, No. 1, 5-18 (2009) http://doi.org/10.1002/zamm.200700158

52.
Existence and Multiplicity Proofs for Semilinear Elliptic Boundary Value Problems by Computer Assistance. DMV Jahresbericht: JB 110, Heft 1 (2008) 19-54.
Download: emp.ps emp.pdf

51.
mit W. N. Everitt, L. Markus und M. Muzzulini: A continuum of unusual selfadjoint linear partial differential operators.
Journal of Computational and Applied Mathematics 208, 164-175 (2007).

50.
mit Ch. Wieners: Numerical enclosures for variational inequalities. Computational Methods in Applied Mathematics, Vol. 7, No. 4, 376-388 (2007).

49.
mit B. Breuer, J. Horák und P. J. McKenna: A computer-assisted existence and multiplicity proof for travelling waves in a nonlinearly supported beam.
J. Differential Equations 224, 60-97 (2006).
Download: travelling.pdf

48.
mit R. C. Brown: An Opial Type Inequality with an Integral Boundary Condition.
Proc. R. Soc. Lond. A 461, 2635-2651 (2005).
Download: opial_type.pdf

47.
mit W. N. Everitt und L. Markus: An Unusual Self-Adjoint Linear Partial Differential Operator.
Trans. Amer. Math. Soc. 367, 1303-1324 (2005).
Download: self-adjoint.pdf

46.
mit E. B. Davies: Spectral Pollution.
IMA Journal of Numerical Analysis 24, 417-438 (2004).

45.
mit B. Breuer und P. J. McKenna: Multiple solutions for a semilinear boundary value problem: a computational multiplicity proof.
J. Differential Equations 195, 243-269 (2003).

44.
mit B. M. Brown und W. D. Evans: Titchmarsh-Sims-Weyl theory for Complex Hamiltonian Systems.
Proc. London Math. Soc. (3) 87, 419-450 (2003).
Download: titchmarsh.pdf

43.
mit J.-R. Lahmann: A computer-assisted instability proof for the Orr-Sommerfeld equation with Blasius profile.
ZAMM 84, No. 3, 188-204 (2004).
Download: orr-sommerfeld.pdf

42.
mit E. Adams: Free Vibrations of Trusses by Fourier Decomposition, and Homotopy Methods for Nonlinear Matrix Eigenvalue Problems, I und II.
J. Math. Anal. Appl. 275, 333-353 (2002) und 276, 64-79 (2002).

41.
mit Ch. Wieners: New solutions of the Gelfand problem.
J. Math. Anal. Appl. 269, 588-606 (2002).

40.
mit Ch. Wieners: Optimal a priori estimates for interface problems.
Numer. Math. 95, 735-759 (2003).

39.
mit P. J. McKenna: Multiple solutions for a semilinear boundary value problem: a computational multiplicity proof.
J. Math. Anal. Appl. 251, No. 2, 710-715 (2000).

38.
mit B. Breuer und P. J. McKenna: Inclusions and Existence Proofs for Solutions of a Nonlinear Boundary Value Problem by Spectral Numerical Methods.
Computing Suppl. 15, 61-77 (2001).

37.
mit Ch. Hipp: Optimal investment for investors with state dependent income, and for insurers.
Finance and Stochastics, Vol. 7, No. 3, 299-321 (2003).

36.
Safe Numerical Error Bounds for Solutions of Nonlinear Elliptic Boundary Value Problems.
In: Symbolic Algebraic Methods and Verification Methods (Eds.: G. Alefeld, J. Rohn, S. Rump, T. Yamamoto), Springer Wien New York, 195-207 (2001).

35.
mit Ch. Hipp: Optimal investment for insurers.
Insurance, Mathematics and Economics 27, 215-228 (2000).

34.
mit H. Behnke, U. Mertins und Ch. Wieners: Eigenvalue inclusions via domain decomposition.
Proc. R. Soc. Lond. A 456, 2717-2730 (2000).

33.
Computer-assisted Enclosure Methods for Elliptic Differential Equations.
Linear Algebra and its Applications 324, 147-187 (2001).

32.
mit J. Lahmann: Das Spektrum der Orr-Sommerfeld-Gleichung mit Blasius-Strömungsprofil.
ZAMM 78, Suppl. 3, S987 - S988 (1998).

31.
mit B. Breuer: Lösungseinschließungen bei einem nichtlinearen Randwertproblem mittels eines Fourierreihenansatzes.
Interner Bericht.

30.
mit R. M. Redheffer: A Class of Second-order Differential Equations.
J. Differential Equations 154, 454-469 (1999).

29.
mit J. Lahmann: On the spectrum of the Orr-Sommerfeld equation on the semi-axis.
Math. Nachr. 216, 145-153 (2000).

28.
mit B. M. Brown, D. K. R. McCormack und W. D. Evans: On the spectrum of second order differential operators with complex coefficients.
Proc. Royal Soc. London. A 455, 1235-1257 (1999).

27.
mit B. M. Brown, M. S. P. Eastham und D. K. R. McCormack: On a new algorithm for the computation of enclosures for the Titchmarsh-Weyl m-function.
Result. Math. 33, 50-64 (1998).

26.
Eigenvalue Problems for Differential Equations.
In: Wavelets, Multilevel Methods and Elliptic PDEs (Eds.: M. Ainsworth , J. Levesley, M. Marletta, W.A. Light), Clarendon Press, Oxford, 39-83 (1997).

25.
Guaranteed Numerical Bounds for Eigenvalues.
In: Spectral theory and computational methods of Sturm-Liouville problems (Eds.: D. Hinton, P. Schaefer), Marcel Dekker, New York, 313-332 (1997).

24.
Enclosure Methods with Existence Proof for Elliptic Differential Equations. Proceedings zu "General Inequalities 7" (Oberwolfach 1995), International Series of Numerical Mathematics, Vol. 123, 347-368 (1997).

23.
Enclosures for Two-Point Boundary Value Problems near Bifurcation Points.
In: Scientific Computing and Validated Numerics, Proceedings of the International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics SCAN-95, held in Wuppertal, Germany, September 26-29, 1995 (Eds.: G. Alefeld, A. Frommer,
B. Lang), Mathematical Research, Volume 90, Akademie Verlag, 265-279 (1996).

22.
Existence Proofs for Elliptic Boundary Value Problems by Numerical Means.
ZAMM 75 SII, S429-S432 (1995).

21.
Lösungseinschließung mit automatischem Existenzbeweis bei elliptischen Randwertproblemen.
In: Jahrbuch Überblicke Mathematik 1995 (Hrsg.: A. Beutelspacher, S.D. Chatterji,
U. Kulisch, R. Liedl), Vieweg Verlag, Braunschweig, 103 - 124 (1995).

20.
Enclosures for Weak Solutions of Nonlinear Elliptic Boundary Value Problems.
In: Inequalities and Applications (Ed.: Ravi P. Agarwal), World Scientific Series In Applicable Analysis, Vol. 3, 505-521 (1994).

19.
Inclusion Methods for Elliptic Boundary Value Problems.
In: Topics in Validated Computations (Ed.: J. Herzberger), Studies in Computational Mathematics 5, North Holland (Elsevier), Amsterdam, 323 - 379 (1994).

18.
Existence and Enclosure Results for Continua of Solutions of Parameter-Dependent Nonlinear Boundary Value Problems.
Journal of Computational and Applied Mathematics 60, 187 - 200 (1995).

17.
mit B. Kalkofen: Optimal Pricing Rules for Private-Value Auctions with Incomplete Information.
Ifo-Studien 1/1996, 77 - 100.

16.
Enclosures for Solutions of Parameter-dependent Nonlinear Elliptic Boundary Value Problems: Theory and Implementation on a Parallel Computer.
Interval Computations 3 (Special Issue on Parallel Algorithms), 106 - 121 (1994).

15.
mit B. M. Brown, W.D. Evans und V.G. Kirby: Safe numerical bounds for the Titchmarsh-Weyl m-function.
Mathematical Proceedings of the Cambridge Philosophical Society 113, 583-599 (1993).

14.
An Existence and Inclusion Method for Two-Point Boundary Value Problems with Turning Points.
ZAMM 74, 615 - 623 (1994).

13.
Numerical Existence Proofs and Explicit Bounds for Solutions of Nonlinear Elliptic Boundary Value Problems.
Computing 49, 25-44 (1992).

12.
Characterization and Computation of Nash-Equilibria for Auctions with Incomplete Information.
International Journal of Game Theory 20, 393-418 (1992).

11.
Continuous Sealed-bid Auctions with Asymmetric Incomplete Information.
Methods of Operations Research 63, 303-312.

10.
Bounds for eigenvalues of second-order elliptic differential operators.
ZAMP 42, 848 - 863 (1991).

9.
Existence proofs in combination with error bounds for approximate solutions of weakly nonlinear second-order elliptic boundary value problems.
ZAMM 71, T660 - T662 (1991).

8.
Explicit H2-estimates and pointwise bounds for solutions of second-order elliptic boundary value problems.
J. Math. Anal. Appl. 165, 36-61 (1992).

7.
Computer-assisted existence proofs for two-point boundary value problems.
Computing 46, 19-34 (1991).

6.
Verified existence and inclusion results for two-point boundary value problems. IMACS Annals on Computing and Applied Mathematics, Baltzer, Vol. 7, 341-355 (1990).

5.
mit M. Goehlen und J. Schröder: A Programmed Algorithm for Existence Proofs for Two-Point Boundary Value Problems. Computing 44, 91-132 (1990).

4.
Existence and inclusion for two-point boundary value problems by numerical means. In: Computational Ordinary Differential Equations (Eds.: J. R. Cash, I. Gladwell), Clarendon Press, Oxford, 415-423 (1992).

3.
Eigenvalue inclusions for second-order ordinary differential operators by a numerical homotopy method.
ZAMP 41, 205-226 (1990).

2.
Shape-Invariant Bounds for Reaction-Diffusion Systems with Unequal Diffusion Coefficients.
J. Differential Equations 73, 82-103 (1988).

1.
Pointwise Bounds for Linear Reaction-Diffusion Systems and an Extension to Nonlinear Problems.
J. Math. Anal. Appl. 135, 88-111 (1988)