Dr Marius Ghergu's web page

Dr. Marius Ghergu

Associate Professor,
School of Mathematics and Statistics, University College Dublin, Ireland




Address

    School of Mathematics and Statistics
    Univesity College Dublin, Belfield campus, Dublin 4, Ireland
    Phone: +353 1716 5739, Fax: +353 1716 1172
    E-mail addresses: firstname[dot]surname[at]ucd[dot]ie

Teaching 2019-2020

  • MATH 10140 Advanced Calculus for Economics and Finance
  • MATH 20180 Foundations for Financial Mathematics
  • MATH 40380 Mathematical Theory for Partial Differential Equations

Research interest

  • Nonlinear Partial Differential Equations of Elliptic and Parabolic Type
  • Harmonic Functions and Classical Potential Theory
  • Stochastic Analysis with Applications in Finance

Books

Publications in Refereed Journals

    2020

  1. M. Ghergu and O. Goubet, Singular solutions of elliptic equations with iterated exponentials, J. Geometric Analysis. (2020), in press [pdf]
  2. M. Ghergu, S. Kim and H. Shahgholian, Isolated singularities for semilinear elliptic systems with power-law nonlinearity, Analysis and PDE. 8 (2020), in press[pdf]
  3. S.J. Gardiner, M. Ghergu and T. Sjödin, Isoperimetric inequalities for Bergman analytic content, Indiana Univ. Math J. (2020), [pdf]
  4. M. Ghergu, P. Karageorgis and G. Singh, Positive solutions for quasilinear elliptic inequalities and systems with nonlocal terms, J. Differential Equations. (2020), in press [pdf]
  5. M. Ghergu, Behavior around isolated singularity for integral inequalities with multiple Riesz potentials, Complex Var. Elliptic Equations. (2020), in press [pdf]
  6. 2019

  7. M. Ghergu, S. D. Taliaferro and I. Verbitsky, Pointwise bounds and blow-up for systems of semilinear elliptic inequalities at an isolated singularity via nonlinear potential estimates, J. d'Analyse Math 12 (2019), [pdf]
  8. M. Ghergu, M. Manolaki, I. Netuka and H. Render, Potential theory and approximation: highlights from the scientific work of Stephen Gardiner, Analysis and Mathematical Physics. 9 (2019), 679-709 [pdf]
  9. M. Ghergu, J. Giacomoni and G. Singh, Global and blow-up radial solutions for quasilinear elliptic systems arising in the study of viscous, heat conducting fluids, Nonlinearity. 32 (2019), 1546-1569 [pdf]
  10. M. Ghergu, J. Giacomoni and Prashanth, Radial singular solutions for the N-Laplace equation with exponential nonlinearities, J. Math. Analysis Applications. 475 (2019), 668-685 [pdf]
  11. M. Ghergu and G. Singh, On a class of mixed Choquard-Schrödinger-Poisson systems, Discrete Cont. Dyn. Systems B. 12 (2019), 297-309 [pdf]
  12. M. Ghergu, S. Kim and H. Shahgholian, Exact behavior around isolated singularity for semilinear elliptic equations with a log-type nonlinearity, Adv. Nonlinear Analysis. 8 (2019), 995-1003 [pdf]
  13. 2018

  14. S.J. Gardiner, M. Ghergu and T. Sjödin, Analytic content and the isoperimetric inequality in higher dimensions, J. Functional Analysis. 275 (2018), 2204-2298 [pdf]
  15. M. Ghergu, Iterated exponential inequalities: a classroom-tailored approach, Int. J. Math. Education Science Technology. 42 (2018), 802-807
  16. 2017

  17. M. Ghergu and S. D. Taliaferro, Pointwise bounds and blow-up for systems of parabolic inequalities and nonlinear heat potential estimates, J. Functional Analysis. 272 (2017), 1301-1339 [pdf]
  18. 2016

  19. M. Ghergu and S. Taliaferro, Pointwise bounds and blow-up for Choquard-Pekar inequalities at an isolated singularity, J. Differential Equations. 261 (2016), 189-217 [pdf]
  20. 2015

  21. M. Ghergu and S. D. Taliaferro, Asymptotic behavior at isolated singularities for solutions of nonlocal semilinear elliptic systems of inequalities, Calc. Variations PDEs 54 (2015), 1243-1273 [pdf]
  22. M. Ghergu and S. D. Taliaferro, Nonexistence of positive supersolutions of nonlinear biharmonic equations without the Maximum Principle, Communications in Partial Differential Equations 40 (2015), 1029-1069 [pdf]
  23. M. Ghergu, On a class of singular elliptic systems, Nonlinear Analysis, 119 (2015), 98-105 [pdf]
  24. 2014

  25. M. Ghergu, V. Liskevich and Z. Sobol, Singular solutions for second-order non-divergence type elliptic inequalities in punctured balls, J. d'Analyse Math. 123 (2014), 251-279 [pdf]
  26. W. Chen, L. Dupaigne and M. Ghergu, A new critical curve for the Lane-Emden system, Discrete Contin. Dyn. Systems (DCDS A), 34 (2014), 2469-2479 [pdf]
  27. 2013

  28. L. Dupaigne, M. Ghergu, O. Goubet and G. Warnault, The Gel'fand problem for the biharmonic operator, Arch. Rational Mech. Analysis 208 (2013), 725-752 [pdf]
  29. M. Ghergu, Singular elliptic systems of Lane-Emden type, Contemp. Math. 595 (2013), 253-262 [pdf]
  30. M. Ghergu and S. D. Taliaferro, Semilinear elliptic inequalities in the exterior of a compact set, Proc. Royal Soc. Edinburgh: Section A (Mathematics) 143 (2013), 563-588 [pdf]
  31. 2012

  32. L. Dupaigne, M. Ghergu, O. Goubet and G. Warnault, Entire large solutions for semilinear elliptic equations, J. Differential Equations 253 (2012), 2224-2251 [pdf]
  33. H. Render and M. Ghergu, Positivity properties for the clamped plate boundary problem on the ellipse and strip, Math. Nachrichten 285 (2012), 1052-1062
  34. M. Ghergu, A biharmonic equation with singular nonlinearity, Proc. Edinburgh Math. Soc. 55 (2012), 155-166 [pdf]
  35. 2011

  36. M. Ghergu, A. Moradifam and S. D. Taliaferro, Isolated singularities of polyharmonic inequalities J. Functional Analysis 261 (2011), 660-680 [pdf]
  37. M. Ghergu, Lane-Emden systems with singular data, Proc. Royal Society of Edinburgh: Section A (Mathematics) 141 (2011), 1279-1294 [pdf]
  38. 2010

  39. S. J. Gardiner and M. Ghergu, Champagne subregions of the unit ball with unavoidable bubbles, Ann. Acad. Sci. Fenn. Math. 35 (2010), 321-329
  40. M. Ghergu, Lane-Emden systems with negative exponents, J. Functional Analysis 258 (2010), 3295-3318
  41. M. Ghergu and V. Radulescu, Turing patterns in a general Brusselator system, Commun. Contemp. Math. 12 (2010), 661-679.
  42. 2009

  43. J. Pres and M. Ghergu, Positive harmonic functions that vanish on a subset of a cylindrical surface, Potential Analysis 31 (2009), 147-181
  44. M. Ghergu, Steady-state solutions for Gierer-Meinhardt type systems with Dirichlet boundary condition, Transactions of the American Mathematical Society 361 (2009), 3953-3976 [pdf]
  45. M. Ghergu, Large time behavior of solutions to degenerate parabolic equations with weights, J. Math. Anal. Appl. 352 (2009), 132-138
  46. M. Ghergu, On the global solutions to a class of strongly degenerate parabolic equations, Nonlinear Analysis 70 (2009), 1430-1442
  47. 2008

  48. M. Ghergu and V. Radulescu, A singular Gierer-Meinhardt system with different source terms, Proc. Royal Society of Edinburgh: Section A (Mathematics) 138 (2008), 1215-1234 [pdf]
  49. M. Ghergu, Non-constant steady states for Brusselator type systems, Nonlinearity 10 (2008), 2331-2345
  50. 2007

  51. M. Ghergu, G. Griso, H. Mechkour and B. Miara, Homogenization of thin piezoelectric perforated shells, M2AN (Mathematical Modelling and Numerical Analysis) 41 (2007), 875-895
  52. L. Dupaigne, M. Ghergu and V. Radulescu, Lane-Emden-Fowler equations with convection and singular potential, J. Math. Pures Appliquees (Journal de Liouville) 87 (2007), 563-581
  53. M. Ghergu and V. Radulescu, Ground state solutions for the singular Lane-Emden-Fowler equation with sublinear convection term, J. Math. Anal. Appl. 333 (2007), 265-273
  54. M. Ghergu and V. Radulescu, On a class of Gierer-Meinhardt systems arising in morphogenesis, C. R. Acad. Sci. Paris, Ser. I 344 (2007), 163-168
  55. 2006

  56. M. Ghergu and V. Radulescu, Singular elliptic problems with lack of compactness, Annali di Matematica Pura ed Applicata 185 (2006), 63-79
  57. 2005

  58. M. Ghergu, F. Cirstea and V. Radulescu, Combined effects of asymptotically linear and singular nonlinearities in bifurcation problems of Lane-Emden-Fowler type, J. Math. Pures Appliquees (Journal de Liouville) 84 (2005), 61-84
  59. M. Ghergu and V. Radulescu, Multiparameter bifurcation and asymptotics for the singular Lane-Emden-Fowler equation with a convection term, Proc. Royal Society of Edinburgh: Section A (Mathematics) 135 (2005), 63-79
  60. M. Ghergu, G. Griso, H. Mechkour and B. Miara, Homogeneisation de coques minces piezoelectriques perforees, Comptes Rendus Mecanique 333 (2005), 249-255
  61. M. Ghergu and V. Radulescu, On a class of sublinear singular elliptic problems with convection term, J. Math. Anal. Appl. 311 (2005), 635-646
  62. 2004

  63. M. Ghergu and V. Radulescu, Bifurcation for a class of singular elliptic problems with quadratic convection term, C. R. Acad. Sci. Paris, Ser. I 338 (2004), 831-836
  64. M. Ghergu and V. Radulescu, Nonradial blow-up solutions of sublinear elliptic equations with gradient term Commun. Pure and Applied Analysis 3 (2004), 465-474
  65. 2003

  66. M. Ghergu and V. Radulescu, Sublinear singular elliptic problems with two parameters, J. Differential Equations 195 (2003), 520-536
  67. M. Ghergu and V. Radulescu, Bifurcation and asymptotics for the Lane-Emden-Fowler equation, C. R. Acad. Sci. Paris, Ser. I 337 (2003), 259-264
  68. M. Ghergu and V. Radulescu, Existence and nonexistence of entire solutions to the logistic differential equation, Abstract and Applied Analysis 17 (2003), 995-1003
  69. M. Ghergu, Small perturbations of degenerate elliptic equations with lack of compactness, Math. Sci. Res. J. 7 (2003), 353-365
  70. M. Ghergu and V. Radulescu, Explosive solutions of semilinear elliptic systems with gradient term, RACSAM Revista Real Academia de Ciencias (Serie A, Matematicas) 97 (2003), 437-445
  71. 2002

  72. M. Ghergu, C. Niculescu and V. Radulescu, Explosive solutions of elliptic equations with absorption and nonlinear gradient term, Proc. Indian Acad. (Math. Sciences) 112 (2002), 1-11