Edit Profile (opens in new tab) Plum, Michael Co-Author Distance Author ID: plum.michael Published as: Plum, Michael; Plum, M. External Links: MGP Documents Indexed: 92 Publications since 1988, including 2 Books and 5 Additional arXiv Preprints 3 Contributions as Editor Reviewing Activity: 159 Reviews Co-Authors: 57 Co-Authors with 66 Joint Publications 1,231 Co-Co-Authors all top 5 Co-Authors 27 single-authored 11 Brown, B. Malcolm 9 Hoang, Vu Phuong 8 McKenna, Patrick Joseph 8 Wood, Ian Geoffrey 7 Wieners, Christian 6 Reichel, Wolfgang 5 Dohnal, Tomáš 5 Nagatou, Kaori 5 Nakao, Mitsuhiro T. 4 Breuer, B. 4 Khrabustovskyi, Andrii 4 Pacella, Filomena 4 Watanabe, Yoshitaka 3 Brown, Malcolm W. 3 Evans, William Desmond 3 Lahmann, Jan-Rainer 3 Pelinovsky, Dmitry Efimovich 3 Radosz, Maria 2 Bandle, Catherine 2 Behnke, Henning 2 Everitt, William Norrie 2 Gilányi, Attila 2 Hipp, Christian 2 Losonczi, László 2 Markus, Lawrence 2 Rockstuhl, Carsten 2 Roth, Dagmar 1 Alefeld, Götz E. 1 Bartsch, Thomas J. 1 Behrndt, Jussi 1 Brown, Richard Clark 1 Contreras, Andres A. 1 Davies, Edward Brian 1 Dorfler, Willy 1 Eastham, Michael S. P. 1 Fazekas, Borbála 1 Goffi, Fatima Z. 1 Göhlen, Michael 1 Kashiwagi, Masahide 1 Kirby, V. G. 1 Lechleiter, Armin 1 Liao, Xian 1 Mertins, Ulrich 1 Mnasri, Karim 1 Muzzulini, M. 1 Oishi, Shin’ichi 1 Páles, Zsolt 1 Redheffer, Raymond M. 1 Rütters, Dagmar 1 Schneider, Guido 1 Schröder, Johann 1 Sekine, Kouta 1 Stohrer, Christian 1 Takeuchi, Airi 1 Tanaka, Kazuaki 1 Venkitakrishnan, Ramakrishna 1 Wunderlich, Jonathan all top 5 Serials 8 Journal of Differential Equations 7 Journal of Mathematical Analysis and Applications 4 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 4 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 3 Computing 3 SIAM Journal on Mathematical Analysis 2 Journal of Computational and Applied Mathematics 2 Journal of the London Mathematical Society. Second Series 2 Mathematische Nachrichten 2 ISNM. International Series of Numerical Mathematics 2 Journal of Elliptic and Parabolic Equations 1 Communications in Mathematical Physics 1 IMA Journal of Numerical Analysis 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Physics Letters. A 1 Acta Cybernetica 1 International Journal of Game Theory 1 Numerical Functional Analysis and Optimization 1 Numerische Mathematik 1 Proceedings of the American Mathematical Society 1 Proceedings of the London Mathematical Society. Third Series 1 Results in Mathematics 1 SIAM Journal on Numerical Analysis 1 Transactions of the American Mathematical Society 1 Insurance Mathematics & Economics 1 Asymptotic Analysis 1 Japan Journal of Industrial and Applied Mathematics 1 Linear Algebra and its Applications 1 NoDEA. Nonlinear Differential Equations and Applications 1 Interval Computations 1 Finance and Stochastics 1 Communications in Contemporary Mathematics 1 Computational Methods in Applied Mathematics 1 Oberwolfach Reports 1 Springer Series in Computational Mathematics 1 Oberwolfach Seminars 1 Advances in Nonlinear Analysis 1 Proceedings A. Royal Society of London all top 5 Fields 53 Partial differential equations (35-XX) 42 Numerical analysis (65-XX) 25 Ordinary differential equations (34-XX) 17 Operator theory (47-XX) 10 Optics, electromagnetic theory (78-XX) 6 Dynamical systems and ergodic theory (37-XX) 6 Computer science (68-XX) 4 Mechanics of deformable solids (74-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 General and overarching topics; collections (00-XX) 3 Real functions (26-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Fluid mechanics (76-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Quantum theory (81-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Operations research, mathematical programming (90-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Difference and functional equations (39-XX) 1 Functional analysis (46-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 71 Publications have been cited 1,057 times in 687 Documents Cited by ▼ Year ▼ Optimal investment for insurers. Zbl 1007.91025 Hipp, Christian; Plum, Michael 162 2000 Explicit \(H_ 2\)-estimates and pointwise bounds for solutions of second- order elliptic boundary value problems. Zbl 0780.35028 Plum, Michael 56 1992 Multiple solutions for a semilinear boundary value problem: a computational multiplicity proof. Zbl 1156.35359 Breuer, B.; McKenna, P. J.; Plum, M. 55 2003 Optimal investment for investors with state dependent income, and for insurers. Zbl 1069.91051 Hipp, Christian; Plum, Michael 53 2003 Spectral pollution. Zbl 1062.65056 Davies, E. B.; Plum, M. 45 2004 Numerical verification methods and computer-assisted proofs for partial differential equations. Zbl 1462.65004 Nakao, Mitsuhiro T.; Plum, Michael; Watanabe, Yoshitaka 43 2019 Existence and enclosure results for continua of solutions of parameter- dependent nonlinear boundary value problems. Zbl 0834.65119 Plum, Michael 35 1995 Computer-assisted enclosure methods for elliptic differential equations. Zbl 0973.65100 Plum, Michael 34 2001 Photonic crystals. Mathematical analysis and numerical approximation. Zbl 1238.78001 Dörfler, Willy; Lechleiter, Armin; Plum, Michael; Schneider, Guido; Wieners, Christian 34 2011 On the spectrum of second-order differential operators with complex coefficients. Zbl 0944.34018 Brown, B. M.; McCormack, D. K. R.; Evans, W. D.; Plum, M. 32 1999 Existence and multiplicity proofs for semilinear elliptic boundary value problems by computer assistance. Zbl 1185.35101 Plum, Michael 31 2008 Bounds for eigenvalues of second-order elliptic differential operators. Zbl 0749.35028 Plum, Michael 28 1991 Characterization and computation of Nash-equilibria for auctions with incomplete information. Zbl 0763.90037 Plum, M. 26 1992 Ground states of a nonlinear curl-curl problem in cylindrically symmetric media. Zbl 1372.35292 Bartsch, Thomas; Dohnal, Tomáš; Plum, Michael; Reichel, Wolfgang 23 2016 Eigenvalue inclusions for second-order ordinary differential operators by a numerical homotopy method. Zbl 0707.65060 Plum, Michael 23 1990 Computer-assisted proofs for semilinear elliptic boundary value problems. Zbl 1186.35073 Plum, Michael 23 2009 A computer-assisted existence and multiplicity proof for travelling waves in a nonlinearly supported beam. Zbl 1104.34034 Breuer, B.; Horák, J.; McKenna, P. J.; Plum, M. 22 2006 Computer-assisted existence proofs for two-point boundary value problems. Zbl 0782.65107 Plum, M. 21 1991 Titchmarsh-Sims-Weyl theory for complex Hamiltonian systems. Zbl 1055.34048 Brown, B. M.; Evans, W. D.; Plum, M. 19 2003 Optimal a priori estimates for interface problems. Zbl 1041.65082 Plum, Michael; Wieners, Christian 18 2003 A computer-assisted instability proof for the Orr-Sommerfeld problem with Poiseuille flow. Zbl 1156.76025 Watanabe, Yoshitaka; Plum, Michael; Nakao, Mitsuhiro T. 15 2009 New solutions of the Gelfand problem. Zbl 1003.65131 Plum, Michael; Wieners, Christian 14 2002 Numerical existence proofs and explicit bounds for solutions of nonlinear elliptic boundary value problems. Zbl 0771.65087 Plum, Michael 14 1992 A uniqueness result for a semilinear elliptic problem: a computer-assisted proof. Zbl 1179.35149 McKenna, P. J.; Pacella, F.; Plum, M.; Roth, D. 13 2009 Guaranteed numerical bounds for eigenvalues. Zbl 0885.47006 Plum, Michael 12 1997 Enclosures for weak solutions of nonlinear elliptic boundary value problems. Zbl 0900.35146 Plum, Michael 12 1994 Surface gap soliton ground states for the nonlinear Schrödinger equation. Zbl 1230.35127 Dohnal, Tomáš; Plum, Michael; Reichel, Wolfgang 11 2011 Localized modes of the linear periodic Schrödinger operator with a nonlocal perturbation. Zbl 1204.34114 Dohnal, Tomáš; Plum, Michael; Reichel, Wolfgang 11 2009 Verified computations of eigenvalue exclosures for eigenvalue problems in Hilbert spaces. Zbl 1294.35047 Watanabe, Yoshitaka; Nagatou, Kaori; Plum, Michael; Nakao, Mitsuhiro T. 11 2014 A computer-assisted proof for photonic band gaps. Zbl 1180.78017 Hoang, Vu; Plum, Michael; Wieners, Christian 10 2009 A computer-assisted uniqueness proof for a semilinear elliptic boundary value problem. Zbl 1253.35046 McKenna, Patrick J.; Pacella, Filomena; Plum, Michael; Roth, Dagmar 9 2012 Eigenvalue inclusions via domain decomposition. Zbl 0993.65120 Behnke, Henning; Mertins, Ulrich; Plum, Michael; Wieners, Christian 8 2000 An unusual self-adjoint linear partial differential operator. Zbl 1081.35022 Everitt, W. N.; Markus, L.; Plum, M. 8 2005 Enclosures for two-point boundary value problems near bifurcation points. Zbl 0849.65060 Plum, Michael 8 1996 Norm bound computation for inverses of linear operators in Hilbert spaces. Zbl 1398.65094 Watanabe, Yoshitaka; Nagatou, Kaori; Plum, Michael; Nakao, Mitsuhiro T. 8 2016 Existence proofs in combination with error bounds for approximate solutions of weakly nonlinear second-order elliptic boundary value problems. Zbl 0735.65084 Plum, M. 8 1991 Verified existence and inclusion results for two-point boundary value problems. Zbl 0784.65067 Plum, Michael 7 1990 A computer-assisted existence proof for Emden’s equation on an unbounded \(L\)-shaped domain. Zbl 1367.35080 Pacella, Filomena; Plum, Michael; Rütters, Dagmar 7 2017 A computer-assisted instability proof for the Orr-Sommerfeld equation with blasius profile. Zbl 1042.65061 Lahmann, Jan-Rainer; Plum, Michael 6 2004 Safe numerical bounds for the Titchmarsh-Weyl \(m(\lambda)\)-function. Zbl 0837.65089 Brown, B. M.; Kirby, V. G.; Evans, W. D.; Plum, M. 5 1993 Operator estimates for homogenization of the Robin Laplacian in a perforated domain. Zbl 1502.35009 Khrabustovskyi, Andrii; Plum, Michael 5 2022 A breather construction for a semilinear curl-curl wave equation with radially symmetric coefficients. Zbl 1386.35275 Plum, Michael; Reichel, Wolfgang 5 2016 Spectrum created by line defects in periodic structures. Zbl 1316.35215 Brown, B. M.; Hoang, V.; Plum, M.; Wood, I. 5 2014 Floquet-Bloch theory for elliptic problems with discontinuous coefficients. Zbl 1247.35073 Brown, B. Malcolm; Hoang, Vu; Plum, Michael; Wood, Ian G. 5 2011 A continuum of unusual self-adjoint linear partial differential operators. Zbl 1134.35041 Everitt, W. N.; Markus, L.; Muzzulini, M.; Plum, M. 4 2007 An existence and inclusion method for two-point boundary value problems with turning points. Zbl 0823.34028 Plum, M. 4 1994 Enclosures for solutions of parameter-dependent nonlinear elliptic boundary value problems: Theory and implementation on a parallel computer. Zbl 0833.65134 Plum, Michael 4 1994 Eigenvalue excluding for perturbed-periodic one-dimensional Schrödinger operators. Zbl 1364.34124 Nagatou, Kaori; Plum, Michael; Nakao, Mitsuhiro T. 4 2012 A programmed algorithm for existence proofs for two-point boundary value problems. Zbl 0703.65043 Göhlen, M.; Plum, M.; Schröder, J. 4 1990 Inclusion methods for elliptic boundary value problems. Zbl 0814.65105 Plum, Michael 3 1994 Inclusions and existence proofs for solutions of a nonlinear boundary value problem by spectral numerical methods. Zbl 0994.65129 Breuer, B.; Plum, M.; McKenna, P. J. 3 2001 On the spectrum of the Orr-Sommerfeld equation on the semiaxis. Zbl 0988.34070 Lahmann, J.; Plum, M. 3 2000 On the spectrum of waveguides in planar photonic bandgap structures. Zbl 1371.78110 Brown, B. M.; Hoang, V.; Plum, M.; Wood, I. 3 2015 Eigenvalue problems for differential equations. Zbl 0886.65108 Plum, Michael 2 1997 Shape-invariant bounds for reaction-diffusion systems with unequal diffusion coefficients. Zbl 0658.35048 Plum, Michael 2 1988 An Opial-type inequality with an integral boundary condition. Zbl 1153.26313 Brown, Richard C.; Plum, Michael 2 2005 Orbital stability investigations for travelling waves in a nonlinearly supported beam. Zbl 1472.35039 Nagatou, K.; Plum, M.; McKenna, P. J. 2 2019 Orbital stability of domain walls in coupled Gross-Pitaevskii systems. Zbl 1387.35430 Contreras, Andres; Pelinovsky, Dmitry E.; Plum, Michael 2 2018 Gap localization of TE-modes by arbitrarily weak defects. Zbl 1379.35095 Brown, B. M.; Hoang, V.; Plum, M.; Radosz, M.; Wood, I. 2 2017 Higher order constitutive relations and interface conditions for metamaterials with strong spatial dispersion. Zbl 07411323 Goffi, Fatima Z.; Khrabustovskyi, Andrii; Venkitakrishnan, Ramakrishna; Rockstuhl, Carsten; Plum, Michael 2 2021 Free and forced vibrations of trusses by Fourier decomposition, and homotopy methods for nonlinear matrix eigenvalue problems. I: Methods. Zbl 1018.74039 Adams, E.; Plum, M. 1 2002 Free and forced vibrations of trusses by Fourier decomposition, and homotopy methods for nonlinear matrix eigenvalue problems. II: Properties and supplements. Zbl 1019.74040 Adams, E.; Plum, M. 1 2002 Pointwise bounds for linear reaction-diffusion systems and an extension to nonlinear problems. Zbl 0669.35050 Plum, Michael 1 1988 Inequalities and applications. Proceedings of the conference on inequalities and applications, Noszvaj, Hungary, September 9–15, 2007. Zbl 1148.26004 1 2009 Existence proofs for elliptic boundary value problems by numerical means. Zbl 0832.35052 Plum, M. 1 1995 Numerical enclosures for variational inequalities. Zbl 1141.65052 Plum, M.; Wieners, Ch. 1 2007 Spectral properties of an elliptic operator with double-contrast coefficients near a hyperplane. Zbl 1341.47058 Khrabustovskyi, Andrii; Plum, Michael 1 2016 Interfaces supporting surface gap soliton ground states in the 1D nonlinear Schrödinger equation. Zbl 1315.34097 Dohnal, Tomáš; Nagatou, Kaori; Plum, Michael; Reichel, Wolfgang 1 2013 Existence and inclusion for two-point boundary value problems by numerical means. Zbl 0767.65065 Plum, Michael 1 1992 On spectral bounds for photonic crystal waveguides. Zbl 1266.78018 Brown, B. Malcolm; Hoang, Vu; Plum, Michael; Wood, Ian G. 1 2009 Approximate nonradial solutions for the Lane-Emden problem in the ball. Zbl 1473.35261 Fazekas, Borbála; Pacella, Filomena; Plum, Michael 1 2022 Operator estimates for homogenization of the Robin Laplacian in a perforated domain. Zbl 1502.35009 Khrabustovskyi, Andrii; Plum, Michael 5 2022 Approximate nonradial solutions for the Lane-Emden problem in the ball. Zbl 1473.35261 Fazekas, Borbála; Pacella, Filomena; Plum, Michael 1 2022 Higher order constitutive relations and interface conditions for metamaterials with strong spatial dispersion. Zbl 07411323 Goffi, Fatima Z.; Khrabustovskyi, Andrii; Venkitakrishnan, Ramakrishna; Rockstuhl, Carsten; Plum, Michael 2 2021 Numerical verification methods and computer-assisted proofs for partial differential equations. Zbl 1462.65004 Nakao, Mitsuhiro T.; Plum, Michael; Watanabe, Yoshitaka 43 2019 Orbital stability investigations for travelling waves in a nonlinearly supported beam. Zbl 1472.35039 Nagatou, K.; Plum, M.; McKenna, P. J. 2 2019 Orbital stability of domain walls in coupled Gross-Pitaevskii systems. Zbl 1387.35430 Contreras, Andres; Pelinovsky, Dmitry E.; Plum, Michael 2 2018 A computer-assisted existence proof for Emden’s equation on an unbounded \(L\)-shaped domain. Zbl 1367.35080 Pacella, Filomena; Plum, Michael; Rütters, Dagmar 7 2017 Gap localization of TE-modes by arbitrarily weak defects. Zbl 1379.35095 Brown, B. M.; Hoang, V.; Plum, M.; Radosz, M.; Wood, I. 2 2017 Ground states of a nonlinear curl-curl problem in cylindrically symmetric media. Zbl 1372.35292 Bartsch, Thomas; Dohnal, Tomáš; Plum, Michael; Reichel, Wolfgang 23 2016 Norm bound computation for inverses of linear operators in Hilbert spaces. Zbl 1398.65094 Watanabe, Yoshitaka; Nagatou, Kaori; Plum, Michael; Nakao, Mitsuhiro T. 8 2016 A breather construction for a semilinear curl-curl wave equation with radially symmetric coefficients. Zbl 1386.35275 Plum, Michael; Reichel, Wolfgang 5 2016 Spectral properties of an elliptic operator with double-contrast coefficients near a hyperplane. Zbl 1341.47058 Khrabustovskyi, Andrii; Plum, Michael 1 2016 On the spectrum of waveguides in planar photonic bandgap structures. Zbl 1371.78110 Brown, B. M.; Hoang, V.; Plum, M.; Wood, I. 3 2015 Verified computations of eigenvalue exclosures for eigenvalue problems in Hilbert spaces. Zbl 1294.35047 Watanabe, Yoshitaka; Nagatou, Kaori; Plum, Michael; Nakao, Mitsuhiro T. 11 2014 Spectrum created by line defects in periodic structures. Zbl 1316.35215 Brown, B. M.; Hoang, V.; Plum, M.; Wood, I. 5 2014 Interfaces supporting surface gap soliton ground states in the 1D nonlinear Schrödinger equation. Zbl 1315.34097 Dohnal, Tomáš; Nagatou, Kaori; Plum, Michael; Reichel, Wolfgang 1 2013 A computer-assisted uniqueness proof for a semilinear elliptic boundary value problem. Zbl 1253.35046 McKenna, Patrick J.; Pacella, Filomena; Plum, Michael; Roth, Dagmar 9 2012 Eigenvalue excluding for perturbed-periodic one-dimensional Schrödinger operators. Zbl 1364.34124 Nagatou, Kaori; Plum, Michael; Nakao, Mitsuhiro T. 4 2012 Photonic crystals. Mathematical analysis and numerical approximation. Zbl 1238.78001 Dörfler, Willy; Lechleiter, Armin; Plum, Michael; Schneider, Guido; Wieners, Christian 34 2011 Surface gap soliton ground states for the nonlinear Schrödinger equation. Zbl 1230.35127 Dohnal, Tomáš; Plum, Michael; Reichel, Wolfgang 11 2011 Floquet-Bloch theory for elliptic problems with discontinuous coefficients. Zbl 1247.35073 Brown, B. Malcolm; Hoang, Vu; Plum, Michael; Wood, Ian G. 5 2011 Computer-assisted proofs for semilinear elliptic boundary value problems. Zbl 1186.35073 Plum, Michael 23 2009 A computer-assisted instability proof for the Orr-Sommerfeld problem with Poiseuille flow. Zbl 1156.76025 Watanabe, Yoshitaka; Plum, Michael; Nakao, Mitsuhiro T. 15 2009 A uniqueness result for a semilinear elliptic problem: a computer-assisted proof. Zbl 1179.35149 McKenna, P. J.; Pacella, F.; Plum, M.; Roth, D. 13 2009 Localized modes of the linear periodic Schrödinger operator with a nonlocal perturbation. Zbl 1204.34114 Dohnal, Tomáš; Plum, Michael; Reichel, Wolfgang 11 2009 A computer-assisted proof for photonic band gaps. Zbl 1180.78017 Hoang, Vu; Plum, Michael; Wieners, Christian 10 2009 Inequalities and applications. Proceedings of the conference on inequalities and applications, Noszvaj, Hungary, September 9–15, 2007. Zbl 1148.26004 1 2009 On spectral bounds for photonic crystal waveguides. Zbl 1266.78018 Brown, B. Malcolm; Hoang, Vu; Plum, Michael; Wood, Ian G. 1 2009 Existence and multiplicity proofs for semilinear elliptic boundary value problems by computer assistance. Zbl 1185.35101 Plum, Michael 31 2008 A continuum of unusual self-adjoint linear partial differential operators. Zbl 1134.35041 Everitt, W. N.; Markus, L.; Muzzulini, M.; Plum, M. 4 2007 Numerical enclosures for variational inequalities. Zbl 1141.65052 Plum, M.; Wieners, Ch. 1 2007 A computer-assisted existence and multiplicity proof for travelling waves in a nonlinearly supported beam. Zbl 1104.34034 Breuer, B.; Horák, J.; McKenna, P. J.; Plum, M. 22 2006 An unusual self-adjoint linear partial differential operator. Zbl 1081.35022 Everitt, W. N.; Markus, L.; Plum, M. 8 2005 An Opial-type inequality with an integral boundary condition. Zbl 1153.26313 Brown, Richard C.; Plum, Michael 2 2005 Spectral pollution. Zbl 1062.65056 Davies, E. B.; Plum, M. 45 2004 A computer-assisted instability proof for the Orr-Sommerfeld equation with blasius profile. Zbl 1042.65061 Lahmann, Jan-Rainer; Plum, Michael 6 2004 Multiple solutions for a semilinear boundary value problem: a computational multiplicity proof. Zbl 1156.35359 Breuer, B.; McKenna, P. J.; Plum, M. 55 2003 Optimal investment for investors with state dependent income, and for insurers. Zbl 1069.91051 Hipp, Christian; Plum, Michael 53 2003 Titchmarsh-Sims-Weyl theory for complex Hamiltonian systems. Zbl 1055.34048 Brown, B. M.; Evans, W. D.; Plum, M. 19 2003 Optimal a priori estimates for interface problems. Zbl 1041.65082 Plum, Michael; Wieners, Christian 18 2003 New solutions of the Gelfand problem. Zbl 1003.65131 Plum, Michael; Wieners, Christian 14 2002 Free and forced vibrations of trusses by Fourier decomposition, and homotopy methods for nonlinear matrix eigenvalue problems. I: Methods. Zbl 1018.74039 Adams, E.; Plum, M. 1 2002 Free and forced vibrations of trusses by Fourier decomposition, and homotopy methods for nonlinear matrix eigenvalue problems. II: Properties and supplements. Zbl 1019.74040 Adams, E.; Plum, M. 1 2002 Computer-assisted enclosure methods for elliptic differential equations. Zbl 0973.65100 Plum, Michael 34 2001 Inclusions and existence proofs for solutions of a nonlinear boundary value problem by spectral numerical methods. Zbl 0994.65129 Breuer, B.; Plum, M.; McKenna, P. J. 3 2001 Optimal investment for insurers. Zbl 1007.91025 Hipp, Christian; Plum, Michael 162 2000 Eigenvalue inclusions via domain decomposition. Zbl 0993.65120 Behnke, Henning; Mertins, Ulrich; Plum, Michael; Wieners, Christian 8 2000 On the spectrum of the Orr-Sommerfeld equation on the semiaxis. Zbl 0988.34070 Lahmann, J.; Plum, M. 3 2000 On the spectrum of second-order differential operators with complex coefficients. Zbl 0944.34018 Brown, B. M.; McCormack, D. K. R.; Evans, W. D.; Plum, M. 32 1999 Guaranteed numerical bounds for eigenvalues. Zbl 0885.47006 Plum, Michael 12 1997 Eigenvalue problems for differential equations. Zbl 0886.65108 Plum, Michael 2 1997 Enclosures for two-point boundary value problems near bifurcation points. Zbl 0849.65060 Plum, Michael 8 1996 Existence and enclosure results for continua of solutions of parameter- dependent nonlinear boundary value problems. Zbl 0834.65119 Plum, Michael 35 1995 Existence proofs for elliptic boundary value problems by numerical means. Zbl 0832.35052 Plum, M. 1 1995 Enclosures for weak solutions of nonlinear elliptic boundary value problems. Zbl 0900.35146 Plum, Michael 12 1994 An existence and inclusion method for two-point boundary value problems with turning points. Zbl 0823.34028 Plum, M. 4 1994 Enclosures for solutions of parameter-dependent nonlinear elliptic boundary value problems: Theory and implementation on a parallel computer. Zbl 0833.65134 Plum, Michael 4 1994 Inclusion methods for elliptic boundary value problems. Zbl 0814.65105 Plum, Michael 3 1994 Safe numerical bounds for the Titchmarsh-Weyl \(m(\lambda)\)-function. Zbl 0837.65089 Brown, B. M.; Kirby, V. G.; Evans, W. D.; Plum, M. 5 1993 Explicit \(H_ 2\)-estimates and pointwise bounds for solutions of second- order elliptic boundary value problems. Zbl 0780.35028 Plum, Michael 56 1992 Characterization and computation of Nash-equilibria for auctions with incomplete information. Zbl 0763.90037 Plum, M. 26 1992 Numerical existence proofs and explicit bounds for solutions of nonlinear elliptic boundary value problems. Zbl 0771.65087 Plum, Michael 14 1992 Existence and inclusion for two-point boundary value problems by numerical means. Zbl 0767.65065 Plum, Michael 1 1992 Bounds for eigenvalues of second-order elliptic differential operators. Zbl 0749.35028 Plum, Michael 28 1991 Computer-assisted existence proofs for two-point boundary value problems. Zbl 0782.65107 Plum, M. 21 1991 Existence proofs in combination with error bounds for approximate solutions of weakly nonlinear second-order elliptic boundary value problems. Zbl 0735.65084 Plum, M. 8 1991 Eigenvalue inclusions for second-order ordinary differential operators by a numerical homotopy method. Zbl 0707.65060 Plum, Michael 23 1990 Verified existence and inclusion results for two-point boundary value problems. Zbl 0784.65067 Plum, Michael 7 1990 A programmed algorithm for existence proofs for two-point boundary value problems. Zbl 0703.65043 Göhlen, M.; Plum, M.; Schröder, J. 4 1990 Shape-invariant bounds for reaction-diffusion systems with unequal diffusion coefficients. Zbl 0658.35048 Plum, Michael 2 1988 Pointwise bounds for linear reaction-diffusion systems and an extension to nonlinear problems. Zbl 0669.35050 Plum, Michael 1 1988 all cited Publications top 5 cited Publications all top 5 Cited by 811 Authors 35 Plum, Michael 34 Nakao, Mitsuhiro T. 26 Lessard, Jean-Philippe 24 Watanabe, Yoshitaka 19 Zhao, Hui 18 Rong, Ximin 16 Oishi, Shin’ichi 11 Kinoshita, Takehiko 11 Mireles-James, Jason D. 11 Reichel, Wolfgang 11 Tanaka, Kazuaki 10 Mederski, Jarosław 10 van den Berg, Jan Bouwe 9 McKenna, Patrick Joseph 9 Qi, Jiangang 9 Sun, Huaqing 9 Yamamoto, Nobito 8 Breden, Maxime 8 Luo, Shangzhen 8 Marletta, Marco 8 Nagatou, Kaori 8 Sekine, Kouta 7 Brown, B. Malcolm 7 Dohnal, Tomáš 7 Khrabustovskyi, Andrii 7 Liu, Xuefeng 7 Ryoo, Cheon Seoung 7 Wanner, Thomas 6 Arioli, Gianni 6 Bi, Junna 6 Boulton, Lyonell 6 Gameiro, Marcio F. 6 Guebbaï, Hamza 6 Guo, Junyi 6 Hipp, Christian 6 Li, Danping 6 Liang, Zhibin 6 Mizuguchi, Makoto 6 Schmidli, Hanspeter 6 Strauss, Michael A. 6 Takayasu, Akitoshi 6 Yan, Shusen 5 Grandits, Peter 5 Koch, Hans-Friedrich 5 Mandel, Rainer 5 Minamoto, Teruya 5 Rump, Siegfried Michael 5 Sander, Evelyn 5 Siu, Tak Kuen 5 Wieners, Christian 5 Xu, Lin 5 Yang, Hailiang 5 Young, Virginia R. 5 Zhang, Xin 4 Bai, Lihua 4 Bartsch, Thomas J. 4 Cancès, Eric 4 Hinton, Don Barker 4 Ortner, Christoph 4 Pacella, Filomena 4 Schneider, Guido 4 Tretter, Christiane 4 Wang, Mingming 4 Yuen, Kam Chuen 3 Azcue, Pablo 3 Bayraktar, Erhan 3 Behncke, Horst 3 Belkina, Tat’yana Andreevna 3 Bieganowski, Bartosz 3 Bögli, Sabine 3 Cai, Shuting 3 Castelli, Roberto 3 Chiu, Mei Choi 3 Church, Kevin E. M. 3 Davies, Edward Brian 3 de Marchis, Francesca 3 Deka, Bhupen 3 Drouot, Alexis 3 Düll, Wolf-Patrick 3 Dusson, Geneviève 3 Elliott, Robert James 3 Gaier, Johanna 3 Gesztesy, Fritz 3 Gómez-Serrano, Javier 3 Guo, Yuxia 3 Hénot, Olivier 3 Hoang, Vu Phuong 3 Hu, Yijun 3 Ianni, Isabella 3 Jaquette, Jonathan 3 Khellaf, Ammar 3 Konyukhova, Nadyezhda B. 3 Kostadinova, Radostina 3 Li, Jingzhi 3 Li, Sheng 3 Liang, Xiaoqing 3 Lin, Xiang 3 Maday, Yvon 3 Mahmoudi, Fethi 3 Meng, Qingbin ...and 711 more Authors all top 5 Cited in 200 Serials 51 Journal of Computational and Applied Mathematics 39 Insurance Mathematics & Economics 30 Journal of Differential Equations 27 Journal of Mathematical Analysis and Applications 16 Japan Journal of Industrial and Applied Mathematics 15 Numerische Mathematik 15 Scandinavian Actuarial Journal 11 Journal of Scientific Computing 10 Applied Mathematics and Computation 10 Applied Numerical Mathematics 10 Journal of Industrial and Management Optimization 9 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 9 Communications in Statistics. Theory and Methods 9 Calculus of Variations and Partial Differential Equations 8 Journal of Functional Analysis 7 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 Mathematics of Computation 7 SIAM Journal on Applied Dynamical Systems 6 Archive for Rational Mechanics and Analysis 6 Journal of Mathematical Physics 6 Nonlinearity 6 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 6 Computing 6 Journal of Economic Theory 6 Numerical Functional Analysis and Optimization 6 Journal of Dynamics and Differential Equations 6 SIAM Journal on Scientific Computing 6 Journal of Systems Science and Complexity 6 ASTIN Bulletin 6 Journal of Computational Dynamics 5 Computers & Mathematics with Applications 5 Integral Equations and Operator Theory 5 Acta Mathematicae Applicatae Sinica. English Series 5 Applied Mathematics Letters 5 Communications in Nonlinear Science and Numerical Simulation 5 North American Actuarial Journal 5 Journal of Spectral Theory 4 SIAM Journal on Numerical Analysis 4 The Annals of Applied Probability 4 Games and Economic Behavior 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Linear Algebra and its Applications 4 SIAM Journal on Mathematical Analysis 4 Discrete and Continuous Dynamical Systems 4 Abstract and Applied Analysis 4 Journal of Inequalities and Applications 4 Stochastic Models 4 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 4 JSIAM Letters 4 SN Partial Differential Equations and Applications 3 Communications in Mathematical Physics 3 International Journal of Control 3 Rocky Mountain Journal of Mathematics 3 Mathematische Nachrichten 3 Proceedings of the American Mathematical Society 3 Physica D 3 Computational Mathematics and Mathematical Physics 3 European Journal of Operational Research 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Bulletin of the American Mathematical Society. New Series 3 NoDEA. Nonlinear Differential Equations and Applications 3 Finance and Stochastics 3 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 3 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 3 Discrete Dynamics in Nature and Society 3 Communications in Contemporary Mathematics 3 The ANZIAM Journal 3 Discrete and Continuous Dynamical Systems. Series B 3 Journal of Fixed Point Theory and Applications 2 Advances in Applied Probability 2 Applicable Analysis 2 Journal of Computational Physics 2 Advances in Mathematics 2 Archiv der Mathematik 2 BIT 2 Journal of Approximation Theory 2 Journal of the London Mathematical Society. Second Series 2 SIAM Journal on Control and Optimization 2 Optimization 2 Economics Letters 2 Numerical Algorithms 2 Indagationes Mathematicae. New Series 2 Journal of Nonlinear Science 2 Computational and Applied Mathematics 2 Economic Theory 2 Journal of Difference Equations and Applications 2 Mathematical Problems in Engineering 2 Mathematical Methods of Operations Research 2 Journal of Mathematical Fluid Mechanics 2 Lobachevskii Journal of Mathematics 2 Annales Henri Poincaré 2 Applied Stochastic Models in Business and Industry 2 Iranian Journal of Science and Technology. Transaction A: Science 2 Advanced Nonlinear Studies 2 Communications on Pure and Applied Analysis 2 Advances in Difference Equations 2 Oberwolfach Reports 2 Stochastics 2 The B. E. Journal of Theoretical Economics 2 European Actuarial Journal ...and 100 more Serials all top 5 Cited in 42 Fields 302 Partial differential equations (35-XX) 223 Numerical analysis (65-XX) 197 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 95 Ordinary differential equations (34-XX) 90 Operator theory (47-XX) 89 Probability theory and stochastic processes (60-XX) 83 Systems theory; control (93-XX) 45 Calculus of variations and optimal control; optimization (49-XX) 43 Optics, electromagnetic theory (78-XX) 36 Dynamical systems and ergodic theory (37-XX) 32 Fluid mechanics (76-XX) 31 Mechanics of deformable solids (74-XX) 24 Statistics (62-XX) 24 Computer science (68-XX) 20 Global analysis, analysis on manifolds (58-XX) 20 Quantum theory (81-XX) 16 Statistical mechanics, structure of matter (82-XX) 16 Operations research, mathematical programming (90-XX) 10 Harmonic analysis on Euclidean spaces (42-XX) 10 Functional analysis (46-XX) 9 Difference and functional equations (39-XX) 7 Approximations and expansions (41-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 5 Integral equations (45-XX) 5 Mechanics of particles and systems (70-XX) 4 Real functions (26-XX) 4 Special functions (33-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 General and overarching topics; collections (00-XX) 2 Potential theory (31-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Abstract harmonic analysis (43-XX) 2 Biology and other natural sciences (92-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 \(K\)-theory (19-XX) 1 Functions of a complex variable (30-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Relativity and gravitational theory (83-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year