
O. Costin, R. Donninger, I. Glogic and M. Huang, On the Stability of
SelfSimilar Solutions to Nonlinear Wave Equations Comm. Math. Phys.,
343 (2016), no. 1, 299–310. CMP

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 748784. CMP

O. Costin,
N. Falkner, J D McNeal, Some generalizations of the
RiemannLebesgue lemma. Amer. Math. Monthly 123 (2016), no. 4,
387–391 MAA

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:
75797621 (2016) (Dec 2015, online)
TAMS arXiv

O. Costin, P.
Ehrlich, H. Friedman, Integration on the Surreals: a
Conjecture of Conway, Kruskal and Norton, submitted, arXiv
 O. Costin, R. Donninger, I
Glogić, M. Huang, On the stability of selfsimilar solutions
to nonlinear wave equations, submitted,
arXiv
 O. Costin, R. Donninger, X.
Xia, A Proof for the Mode Stability of a Selfsimilar Wave
Map, Nonlinearity, V. 29, no. 8, pp. 24512473 arXiv
 O. Costin
and M. Huang, Decay estimates for Onedimensional wave
equations with inverse power potentials. Trans. Amer. Math.
Soc. 367 (2015) arXiv
 O. Costin, X. Xia, From
Taylor series of analytic functions to their global analysis,
Nonlinear Anal. 119 (2015), 106–114, arXiv
 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
 O. Costin,
H. Friedman, Foundational aspects of singular integrals
Journal of Functional Analysis 267 (2014) 4732–4752. arXiv

O. Costin, M.
Huang Decay estimates for Onedimensional wave equations with
inverse power potentials, to appear in TAMS arXiv
 O. Costin,
T. Kim, S. Tanveer, A quasisolution approach to nonlinear
problems  the case of Blasius similarity solution, Fluid Dyn.
Res. 46 (2014), no. 3, arXiv


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. 665704 (2014). arXiv

O. Costin,
R.D. Costin, M. Huang, Tronquee solutions of the Painleve
equation P1, Constr. Approx. 41 (2015), no. 3, 467–494. pdf
 O. Costin
and G. Giacomin, "Oscillatory Critical Amplitudes in
Hierarchical models and the Harris Function of Branching
Processes", J. Stat. Phys, 150, 3, pp 471486 (2013).
arXiv
 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
 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
 O. Costin,
L. Dupaigne and O. Goubet, "Uniqueness of large solutions". J.
Math. Analysis and Applications, 395,2, pp. 806812 (2012). arXiv
 Semiclassical
low energy scattering for onedimensional Schrödinger
operators with exponentially decaying potentials (with R
Donninger, W Schlag and S Tanveer), Ann. Inst. Henri Poincaré , 13, 6, pp
13711426 (2012). .arXiv
 O. Costin, M Huang and W
Schlag, On the spectral properties of L_{±} in
three dimensions Nonlinearity 25, pp. 125164
(2012) arXiv
 O. Costin,
H. Parkh and Y. Takei, Borel summability of the heat equation
with variable coefficients, J. Diff. Eq. Volume 252, 4,
pp. 30763092 (2012).
 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
 Gamow
vectors and Borel summability in a class of quantum systems
(with M Huang) J. Stat. Phys, Vol. 144, Number 4, pp. 846871
(2011)
Springer link, free access
 Global
behavior of solutions of nonlinear ODEs: first order equations
(with M. Huang and F. Fauvet), submitted .arXiv
 Geometric
construction and analytic representation of Julia sets of
polynomial maps (with M. Huang) Nonlinearity 24 (2011), no. 4,
13111327 .arXiv
 Integral
equation representation and longer time existence solutions of
3d NavierStokes (With G. Luo and S. Tanveer) Comm. Contemp.
Math, 13 (3), pp 407462 (2011) ArXiv
 Boundary
blowup solutions in the unit ball : asymptotics, uniqueness
and symmetry (with L. Dupaigne) J. Differential
Equations 249 (2010), no. 4, 931964. arXiv
 Ionization of
Coulomb systems in ℝ^{3} by time periodic forcing
of arbitrary size (with J. L. Lebowitz and S.
Tanveer, Comm. Math. Phys. 296 (2010), no. 3,
681738 Arxiv)
 Exact results for ionization of model
atomic systems (with J.L. Lebowitz, C. Stucchio
and S. Tanveer, J. Math. Phys., 51, 1 (2010). pdf

Resurgence of the fractional polylogarithms (with S.
Garoufalidis) , Math. Res. Lett. 16 (2009), no. 5,
81782. arXiv
 Short time existence
and Borel summability in the NavierStokes equation in ℝ^{3}
(with S. Tanveer). Comm. Partial Differential Equations 34
(2009), no. 79, 785817 pdf
 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
 Behavior of
lacunary series at the natural boundary (with M. Huang,
Advances in Mathematics 222 (2009) 1370–1404) Elsevier
link pdf
 Ionization
in damped harmonic fields (with M. Huang and Z. Qiu, J. Phys
A: Math. Theor, 42 (2009)) ArXiV link J.
Phys
A link
 An Integral equation Approach to Smooth 3D NavierStokes
Solution (with G. Luo and S. Tanveer, Physica Scripta T 132,
2008).
 Resurgence of
the EulerMaclaurin summation formula (with S.
Garoufalidis, Annales
de l' Institut Fourier 58 893914 (2008) pdf
 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
 Ionization
in a 1dimensional dipole model (with J. L. Lebowitz and
C. Stucchio), Reviews in Mathematical Physics, 20
No: 7 , pp. 835872 (2008). pdf
 Sharp
HardyLeray inequality for axisymmetric divergencefree
fields (with V. Maz'ya,) Calc. Var. Partial
Differential Equations 32 (2008), no. 4,) pdf
 Divergent
expansions, Borel summability and the 3D
NavierStokes Equation (With G. Luo and S. Tanveer, Phil.
Trans. R. Soc. A 366, pp 27752788 (2008)pdf.
 Resurgence
of the KontsevitchZagier power series (with S.
Garoufalidis, to appear in Annales de l'Institut Fourier) pdf
 Global
reconstruction
of analytic functions from local expansions and a new
generalmethod of converting sums into integrals
(submitted) pdf
 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. 56,
937948) pdf
 Borel
summability and Lindstedt series (with G. Gallavotti, G.
Gentile and A. Giuliani, Comm. Math. Phys. v.269, 1;
175193 (2007)) pdf
 Nonlinear evolution PDEs
in ℝ^{+}×ℂ^{d} : existence and
uniqueness of solutions, asymptotics and Borel
summability (with S. Tanveer, Ann. Inst.
H. Poincaré Anal. Nonlin., 24, no. 5, pp. 795823 (2007))
pdf
 Singularity
barriers
and Borel plane analytic properties of 1^{+}
difference equations ( Recent Trends in Exponential
Asymptotics, Publ. RIMS 1424, (2005)) pdf
 Complex Singularity Analysis
for a nonlinear PDEs (with S
Tanveer, Comm. Partial Differential Equations 31, no.
46, 593637 (2006)) pdf
 Analytic
methods
for obstruction to integrability in discrete dynamical
systems
(with M. Kruskal, Comm. Pure Appl. Math. 58
(2005), no. 6, 723749) pdf
 Analyzable
functions
and Applications, AMS Contemporary Mathematics, vol
373
(with M. Kruskal and A. Macintyre
(editors))
 Topological construction of
transseries and introduction to generalized Borel
summability (AMS CONM series vol. 373,
137177) pdf
 On the Construction of
Particle Distributions with Specified Single and
Pair Densities (with J. L.
Lebowitz, J. Phys. Chem. B.; 2004; 108(51);
1961419618) pdf
 Analyzability
in the context of PDEs and applications
(with Saleh Tanveer; Annales Fac. Sci. Toulouse,
V XIII, Fasc. 4, pp.539549 (2004); pdf
 Time asymptotics of the Schrödinger wave function in
timeperiodic 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, 14 283310 (2004). pdf
 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
 Transition to the continuum
of a particle in timeperiodic 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
 Borel summation of adiabatic
invariants (with L. Dupaigne and M.
D. Kruskal, Nonlinearity 17 No 4
15091519 (2004) ) pdf
 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,
3633641 (2004).) pdf
 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 89438951
(2002)) pdf
 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): 14551462
(2002)) .pdf
 Asymptotic properties of a
family of solutions of the Painleve equation PVI (with R D
Costin, IMRN No 22 pp 11671182 (2002)) .pdf
 On the formation of
singularities of solutions of nonlinear
differential systems in antistokes directions
(with R. D. Costin, Inventiones Mathematicae 145,
3, pp 425485 (2001)) .pdf
(Copyright owned
by Inventiones)
 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 126 (2001)) pdf
 Existence and uniqueness of
solutions of nonlinear evolution systems of nth
order partial differential equations in the complex plane (with
S. Tanveer) .pdf
 Resonance Theory for Schrödinger
Operators (with
A.
Soffer; Commun. Math. Phys. 224 (2001)) pdf
 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
405411 (2001)) pdf
 Existence and uniqueness for
a class of nonlinear higherorder partial
differential equations in the complex plane
(with Saleh Tanveer. Communications on Pure and
Applied Mathematics, Vol. LIII, 0001 0026 (2000)) pdf
 Exact Results for the
Ionization of a Model Quantum System
(with A. Rokhlenko and J. Lebowitz) J. Phys. A:
Math. Gen. 33 pp. 19 (2000) pdf
 On the complete ionization
of a periodically perturbed quantum system
(with A. Rokhlenko and J. Lebowitz) (CRM
Proceedings and Lecture Notes 27 pp 5161
(2001)) pdf
 On optimal truncation of
divergent series solutions of nonlinear differential
systems; Berry smoothing. (with
Martin D. Kruskal, Proc. R. Soc. Lond. A 455,
19311956 (1999) .pdf
 Correlation between pole
location and asymptotic behavior for Painlevé I
solutions (Comm. Pure and
Appl. Math. Vol. LII, 04610478 (1999)) .ps.gz
.dvi.gz
 Singular normal form for the
Painleve equation P1 (with R. D.
Costin, Nonlinearity Vol 11, No. 5 pp.
11951208 (1998)) .pdf
 On Borel summation and
Stokes phenomena of nonlinear differential systems
( Duke Math. J. vol 93, No2 (1998)) .ps.gz
dvi.gz
 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
 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
)
 Exponential asymptotics,
transseries, and generalized Borel summation for
analytic rank one systems of ODE's
(IMRN 8, (1995)) .ps.gz
 Gaussian fluctuations in
random matrices (with Joel
Lebowitz, Phys.Rev.Lett v 75 no 1 (1995)) pdf
 Limit probability
distributions for an infinite order phas transition
model J.
Stat.Phys.64 1/2 jpg
(abstract)
 Infinite order phase transition in a
classical spin system J. Stat.Phys.59 5/6 jpg
(abstract)
 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
DMS0103807, DMS0100495, DMS0406193, and DMS0600369, DMS1515755
and a Guggenheim fellowship.
Contact Information

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The Ohio State University
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