Ohio State University 

  1. O. Costin, R. Donninger, I. Glogic and M. Huang, On the Stability of Self-Similar Solutions to Nonlinear Wave Equations Comm. Math. Phys., 343 (2016), no. 1, 299–310. CMP
  2. O. Costin, M.B. Gordy, M. Huang, P J Szerszen, Expectations of Functions of Stochastic Time with Application to Credit Risk Modeling, Mathematical Finance, vol. 26, no 4, pp 748--784. CMP
  3. O. Costin, N. Falkner, J D McNeal, Some generalizations of the Riemann-Lebesgue lemma. Amer. Math. Monthly 123 (2016), no. 4, 387–391 MAA
  4. O. Costin, R. D. Costin and M. Huang, A direct method to find Stokes multipliers in closed form for P$ _1$ and more general integrable systems, Trans. Amer. Math. Soc vol: 368 Issue: 11 pp: 7579-7621 (2016) (Dec 2015, online) TAMS arXiv
  5. O. Costin, P. Ehrlich, H. Friedman, Integration on the Surreals: a Conjecture of Conway, Kruskal and Norton, submitted,  arXiv
  6. O. Costin, R. Donninger, I Glogić, M. Huang, On the stability of self-similar solutions to nonlinear wave equations, submitted, arXiv
  7. O. Costin, R. Donninger, X. Xia, A Proof for the Mode Stability of a Self-similar Wave Map, Nonlinearity, V. 29, no. 8, pp. 2451--2473  arXiv
  8. O. Costin and M. Huang, Decay estimates for One-dimensional wave equations with inverse power potentials. Trans. Amer. Math. Soc. 367 (2015)  arXiv
  9. O. Costin, X. Xia, From Taylor series of analytic functions to their global analysis, Nonlinear Anal. 119 (2015), 106–114, arXiv
  10. O. Costin, S. Tanveer, Analytical approximation of Blasius' similarity solution with rigorous error bounds, SIAM J. Math. Anal. 46 (2014), no. 6, 3782–3813,  arXiv
  11. O. Costin, H. Friedman, Foundational aspects of singular integrals Journal of Functional Analysis 267 (2014) 4732–4752. arXiv
  12. O. Costin, M. Huang Decay estimates for One-dimensional wave equations with inverse power potentials, to appear in TAMS arXiv
  13. O. Costin, T. Kim, S. Tanveer, A quasi-solution approach to nonlinear problems - the case of Blasius similarity solution, Fluid Dyn. Res. 46 (2014), no. 3, arXiv

  14. O. Costin, M. Huang and S. Tanveer, Proof of the Dubrovin conjecture and analysis of the tritronquée solutions of $P_I$, Duke Math Journal, 163, 4, pp. 665-704 (2014). arXiv
  15. O. Costin, R.D. Costin, M. Huang, Tronquee solutions of the Painleve equation P1, Constr. Approx. 41 (2015), no. 3, 467–494. pdf
  16. O. Costin and G. Giacomin, "Oscillatory Critical Amplitudes in Hierarchical models and the Harris Function of Branching Processes", J. Stat. Phys, 150, 3, pp 471--486 (2013). arXiv
  17. O. Costin, S. Tanveer, M. I. Weinstein, The lifetime of shape oscillations of a bubble in an unbounded, inviscid and compressible fluid with surface tension, SIAM J. Math. Anal. 45 (2013), no. 5, 2924–2936,  arXiv
  18. O. Costin, J. L. Lebowitz, G. Speer, A. Troiani, "The blockage problem", Bull. Inst. Math. Acad. Sinica, Vol 8 no 1. (dedicated to SRS Varadhan) (2013). arXiv
  19. O. Costin, L. Dupaigne and O. Goubet, "Uniqueness of large solutions". J. Math. Analysis and Applications, 395,2, pp. 806--812 (2012). arXiv
  20. Semiclassical low energy scattering for one-dimensional Schrödinger operators with exponentially decaying potentials (with R Donninger, W Schlag and S Tanveer), Ann. Inst. Henri Poincaré , 13, 6, pp 1371--1426 (2012). .arXiv
  21. O. Costin, M Huang and W Schlag, On the spectral properties of L± in three dimensions  Nonlinearity 25, pp. 125-164 (2012)  arXiv  
  22. O. Costin, H. Parkh and Y. Takei, Borel summability of the heat equation with variable coefficients, J. Diff. Eq. Volume 252, 4, pp.  3076-3092 (2012).
  23. O. Costin, M. Huang and F.  Fauvet, Global behavior of solutions of nonlinear ODEs: first order equations.  Int Math Res Notices first published online October 31, 2011 doi:10.1093/imrn/rnr203
  24. Gamow vectors and Borel summability in a class of quantum systems (with M Huang) J. Stat. Phys, Vol. 144, Number 4, pp. 846-871 (2011) Springer link, free access
  25. Global behavior of solutions of nonlinear ODEs: first order equations (with M. Huang and F. Fauvet), submitted .arXiv
  26. Geometric construction and analytic representation of Julia sets of polynomial maps (with M. Huang) Nonlinearity 24 (2011), no. 4, 1311--1327 .arXiv
  27. Integral equation representation and longer time existence solutions of 3-d Navier-Stokes (With G. Luo and S. Tanveer) Comm. Contemp. Math, 13 (3), pp 407-462 (2011) ArXiv
  28. Boundary blow-up solutions in the unit ball : asymptotics, uniqueness and symmetry (with  L. Dupaigne) J. Differential Equations 249 (2010), no. 4, 931--964. arXiv
  29. Ionization of Coulomb systems in ℝ3 by time periodic forcing of arbitrary size (with J. L. Lebowitz and S. Tanveer,  Comm. Math. Phys. 296 (2010), no. 3, 681--738 Arxiv)
  30. Exact results for ionization of model atomic systems (with  J.L. Lebowitz, C. Stucchio and S. Tanveer, J. Math. Phys., 51, 1 (2010). pdf
  31. Resurgence of the fractional polylogarithms (with S. Garoufalidis) , Math. Res. Lett. 16 (2009), no. 5, 817--82. arXiv
  32. Short time existence and Borel summability in the Navier-Stokes equation in ℝ3 (with S. Tanveer). Comm. Partial Differential Equations 34 (2009), no. 7-9, 785--817 pdf
  33. Semiclassical analysis of low and zero energy scattering for one dimensional Schrodinger operators with inverse square potentials (with  W. Schlag, W. Staubach,  & S. Tanveer, J. Functional Analysis, special issue dedicated to Paul Malliavin, 255, (2008). arXiv
  34. Behavior of lacunary series at the natural boundary (with M. Huang, Advances in Mathematics 222 (2009) 1370–1404) Elsevier link  pdf
  35. Ionization in damped harmonic fields (with M. Huang and Z. Qiu, J. Phys A: Math. Theor, 42 (2009))  ArXiV link    J. Phys A link  
  36. An Integral equation Approach to Smooth 3-D Navier-Stokes Solution (with G. Luo and S. Tanveer, Physica Scripta T 132, 2008).
  37. Resurgence of the Euler-Maclaurin summation formula (with S. Garoufalidis, Annales de l' Institut Fourier 58  893-914 (2008pdf
  38. Nonlinear Stokes phenomena in first or second order differential equations (Algebraic Analysis of Differential Equations, T. Aoki, H. Majima, Y. Takei & N. Tose (Eds.), Springer (2008)) pdf
  39. Ionization in a 1-dimensional dipole model (with J. L. Lebowitz and C. Stucchio),   Reviews in Mathematical Physics, 20 No: 7 , pp. 835-872 (2008) pdf
  40. Sharp Hardy-Leray inequality for axisymmetric divergence-free fields (with V. Maz'ya,)  Calc. Var. Partial Differential Equations 32 (2008), no. 4,pdf
  41. Divergent expansions, Borel summability and the 3-D  Navier-Stokes Equation (With G. Luo and S. Tanveer, Phil. Trans. R. Soc. A 366, pp 2775-2788 (2008)pdf.
  42. Resurgence of the Kontsevitch-Zagier power series (with S. Garoufalidis, to appear in Annales de l'Institut Fourier) pdf
  43. Global  reconstruction of analytic functions from local expansions and a new generalmethod of converting sums into integrals (submitted)  pdf
  44. On the proof of universality for orthogonal and symplectic ensembles in random matrix theory (with P. Deift and D. Gioev J. Stat. Phys. 129 (2007), no. 5-6, 937--948) pdf
  45. Borel summability and Lindstedt series  (with G. Gallavotti, G. Gentile and A. Giuliani, Comm. Math. Phys. v.269, 1; 175--193 (2007))  pdf
  46. Nonlinear evolution  PDEs in ℝ+×ℂd :  existence and uniqueness of solutions, asymptotics and Borel summability (with S. Tanveer, Ann. Inst. H. Poincaré Anal. Nonlin., 24, no. 5, pp. 795--823 (2007)) pdf
  47. Singularity barriers and Borel plane analytic properties of 1+ difference equations ( Recent Trends in Exponential Asymptotics, Publ. RIMS 1424, (2005))  pdf
  48. Complex Singularity Analysis for a nonlinear PDEs   (with S Tanveer, Comm. Partial Differential Equations 31, no. 4-6, 593--637 (2006))   pdf
  49. Analytic methods for obstruction to integrability in discrete dynamical systems   (with M. Kruskal, Comm. Pure Appl. Math. 58 (2005), no. 6, 723--749)  pdf
  50. Analyzable functions and Applications, AMS Contemporary Mathematics, vol 373   (with M. Kruskal and A. Macintyre (editors)) 
  51. Topological construction of transseries and introduction to generalized Borel summability (AMS CONM series vol. 373, 137--177)   pdf
  52. On the Construction of Particle Distributions with Specified Single and Pair Densities   (with J. L. Lebowitz, J. Phys. Chem. B.; 2004; 108(51); 19614-19618)  pdf
  53. Analyzability in the context of PDEs and applications    (with Saleh Tanveer; Annales Fac. Sci. Toulouse, V XIII, Fasc. 4, pp.539--549 (2004); pdf
  54. Time asymptotics of the Schrödinger wave function in time-periodic potentials     (with R D Costin and J L Lebowitz, J. Stat. Phys., special issue dedicated to Elliott Lieb on the occasion of his 70th birthday, 1--4 283-310 (2004).  pdf
  55. Failure of analytic hypoellipticity in a class of PDOs   (with R. D. Costin, Annali della Scuola Normale Superiore di Pisa, Serie V. Vol II. Fasc. I (2003)) pdf
  56. Transition to the continuum of a particle in time-periodic potentials,    (with R. D. Costin and J L Lebowitz in Advances in Differential Equations and Mathematical Physics,   AMS Contemporary Mathematics series ed. Karpeshina, Stolz, Weikard, and Zeng 2003)  pdf
  57. Borel summation of adiabatic invariants (with  L. Dupaigne and M. D. Kruskal, Nonlinearity  17  No 4 1509-1519 (2004) ) pdf
  58. Rigorous bounds of Stokes constants for some nonlinear ODEs at rank one irregular singularities   (with R. D. Costin and M Kohut,  Proc. R. Soc. Lond. A 460, 363--3641 (2004).) pdf
  59. Decay versus survival of a localized state subjected to harmonic forcing: exact results   (with  J L Lebowitz and A Rokhlenko, J. Phys. A: Math. Gen. 35, pp 8943-8951 (2002)) pdf
  60. Movable singularities of solutions of difference equations in relation to solvability and a study of a superstable fixed point   (with M D Kruskal,  Theoretical and Mathematical Physics, 133 (2): 1455-1462 (2002))  .pdf
  61. Asymptotic properties of a family of solutions of the Painleve equation PVI   (with R D Costin,  IMRN No 22 pp 1167-1182 (2002)) .pdf
  62. On the formation of singularities of solutions of  nonlinear differential systems in antistokes directions  (with R. D. Costin,  Inventiones Mathematicae 145, 3, pp 425-485 (2001)) .pdf    (Copyright owned by Inventiones)
  63. Evolution of a model quantum system under time periodic forcing: conditions for complete ionization   (With R. D. Costin,  A. Rokhlenko and J. Lebowitz; Comm. Math. Phys.  221, 1 pp 1-26 (2001)) pdf
  64. Existence and uniqueness of solutions of nonlinear evolution systems of n-th order   partial differential  equations in the complex plane (with S. Tanveer)  .pdf
  65. Resonance Theory for Schrödinger Operators (with A. Soffer; Commun. Math. Phys. 224 (2001)) pdf
  66. Nonperturbative analysis of a model quantum system under time periodic forcing   (With R. D. Costin, A. Rokhlenko and J. Lebowitz; Comptes Rendus Acad. Sci. Serie I, 332 5 pp 405-411 (2001)) pdf
  67. Existence and uniqueness for a class of nonlinear higher-order partial differential equations in the complex plane   (with Saleh Tanveer. Communications on Pure and Applied Mathematics, Vol. LIII, 0001- 0026 (2000)) pdf
  68. Exact Results for the Ionization of a Model Quantum System   (with A. Rokhlenko and J. Lebowitz) J. Phys. A: Math. Gen.  33 pp. 1--9 (2000) pdf
  69. On the complete ionization of a periodically perturbed  quantum system   (with A. Rokhlenko and J. Lebowitz) (CRM  Proceedings and Lecture Notes 27 pp 51--61 (2001)) pdf
  70. On optimal truncation of divergent series solutions of nonlinear differential systems; Berry smoothing.   (with Martin D. Kruskal, Proc. R. Soc. Lond. A  455, 1931-1956 (1999)  .pdf
  71. Correlation between pole location and asymptotic behavior for Painlevé I solutions   (Comm.  Pure and Appl. Math. Vol. LII, 0461-0478 (1999)) .ps.gz .dvi.gz
  72. Singular normal form for the Painleve equation P1   (with R. D. Costin,  Nonlinearity  Vol 11, No. 5 pp.  1195-1208 (1998))  .pdf
  73. On Borel summation and Stokes phenomena of nonlinear differential systems   ( Duke Math. J. vol 93, No2 (1998)) .ps.gz dvi.gz
  74. Optimal uniform estimates and rigorous asymptotics beyond all orders for a class of ODE's   (with Martin D. Kruskal, Proc. Roy. Soc. Lond. 452 (1996)) .ps.gz
  75. Rigorous WKB for finite order linear recurrence relations with smooth coefficients   (with R.D. Costin, SIAM.J.Math.Anal. v27 no1 (1996)) .ps.gz (or abstract jpg )
  76. Exponential asymptotics, transseries, and generalized Borel summation for analytic rank one systems of ODE's     (IMRN 8, (1995)) .ps.gz
  77. Gaussian fluctuations in random matrices   (with Joel Lebowitz, Phys.Rev.Lett v 75  no 1 (1995)) pdf
  78. Limit probability distributions for an infinite order phas transition model   J. Stat.Phys.64 1/2 jpg (abstract)
  79. Infinite order phase transition in a classical spin system   J. Stat.Phys.59 5/6 jpg (abstract)
  80. The infinite coordinationl limit for classical spin systems on irregular lattices    J. Phys. A:Math.Gen.19 jpg (abstract)
Part of the recent research was supported by the NSF awards DMS-0103807, DMS-0100495, DMS-0406193, and DMS-0600369, DMS-1515755 and a Guggenheim fellowship.

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