Grants 

• NSF DMS-2317068 (2023-2024), conference grant to support Fall 2023 Mathematics Conference: Differential Equations and Dynamical Systems and Applications. PI: A. Sukhtayev;  
• NSF DMS-1910820 (09.01.2019-08.31.2024), 'Spectral Stability and Oscillations of Dynamical Systems, Boltzmann-Like Models'. PI: A. Sukhtayev; 
• NSF DMS-1919555 (2019-2020), conference grant to support Fall 2019 Mathematics Conference: Differential Equations and Dynamical Systems and Applications. Co-PI: A. Sukhtayev;  

Curriculum Vitae




Publications

24. Splitting Quantum Graphs, submitted (with N. Smith)

25. Spectral decomposition and decay to grossly determined solutions for a simplified BGK model, J. Funct. Anal. 287 (2024), no. 8, Paper No. 110546, 66 pp. (with K. Zumbrun)

26. Fredholm determinants, Evans functions and Maslov indices for partial differential equations, Mathematische Annalen, 2023 (with G. Cox, Y. Latushkin)

27. Renormalized Oscillation Theory for Singular Linear Hamiltonian Systems, J. Funct. Anal. 283 (2022), no. 3, Paper No. 109525, 74 pp. (with P. Howard)

28. Renormalized oscillation theory for linear Hamiltonian systems on [0,1] via the Maslov index, Journal of Dynamics and Differential Equations, 2022 (with P. Howard) arXiv:1808.08264

29. A dynamical approach to semilinear elliptic equations, Annales de l'Institut Henri Poincar\'e C, Analyse Non Lin\'eaire, 38 (2021), no. 2, 421-450 (with M. Beck, G. Cox, C. Jones, Y. Latushkin) arXiv:1907.09986

30. Exponential dichotomies for elliptic PDE on radial domains, In: D\"orfler W. et al. (eds) Mathematics of Wave Phenomena. Trends in Mathematics. Birkh\"auser, Cham. (2020), 49-68 (with M. Beck, G. Cox, C. Jones, Y. Latushkin) arXiv:1907.10372

31. A Sturm-Liouville theorem for quadratic operator pencils, Journal of Differential Equations, Volume 268, Issue 7, 2020, 3848-3879 (with K. Zumbrun) arXiv:1907.05679

32. The Maslov and Morse Indices for Sturm-Liouville Systems on the Half-Line, Discr. Cont. Dynam. Systems Ser. A, 2020, 40 (2) : 983-1012 (with P. Howard) arXiv:1903.07583

33. Spectral stability of hydraulic shock profiles, Physica D: Nonlinear Phenomena, 405 (2020), 132360, 9 pp. (with Z. Yang, K. Zumbrun) arXiv:1810.01490

34. Instability of pulses in gradient reaction-diffusion systems: A symplectic approach, Philosophical Transactions of the Royal Society A 376 (2018), no. 2117
    (with M. Beck, G. Cox, C. Jones, Y. Latushkin, K. McQuighan) arXiv:1705.03861

35. Diffusive stability of spatially periodic patterns with a conservation law, preprint arXiv:1610.05395

36. Diffusive stability of spatially periodic solutions of the Brusselator model, Communications in Mathematical Physics 358 (2018), no. 1, 1-43 (with K. Zumbrun, S. Jung, R. Venkatraman) arXiv:1608.08476

37. The Maslov and Morse indices for Schr\"odinger operators on $\mathbb{R}$, Indiana University Mathematics Journal 67 (2018), no. 5, 1765-1815 (with P. Howard, Y. Latushkin) arXiv:1608.05692

38. The Morse and Maslov Indices for Schr\"odinger Operators, Journal d'Analyse Mathematique 135 (2018), no. 1, 345-387 (with Y. Latushkin, S. Sukhtaiev) arXiv:1411.1656

39. The Maslov and Morse indices for Lagrangian pairs on $\mathbb{R}^{2n}$, J. Math. Anal. Appl. 451 (2017), no. 2, 794-821 (with P. Howard, Y. Latushkin) arXiv:1608.00632

40. Hadamard-type formulas via the Maslov form, J. Evol. Equ. 17 (2017), no. 1, 443-472 (with Y. Latushkin) arXiv:1601.07509

41. The Maslov and Morse indices for Schr\"odinger Operators on $[0,1]$, Journal of Differential Equations 260 (2016), no. 5, 4499-4549 (with P. Howard) arXiv:1603.02648

42. The Morse and Maslov indices for multidimensional Schr\"odinger operators with matrix-valued potentials, Trans. Amer. Math. Soc. 368 (2016), no. 11, 8145-8207
    (with G. Cox, C. Jones, Y. Latushkin) arXiv:1408.1103

43. Vakhitov-Kolokolov and energy vanishing conditions for linear instability of solitary waves in models of classical self-interacting spinor fields, Nonlinearity 28 (2015), 577--592
    (with G. Berkolaiko, A. Comech) arXiv:1306.5150

44. The Evans function and the Weyl-Titchmarsh function, in Special issue on stability of travelling waves, Disc. Cont. Dynam. Syst. Ser. S 5 (2012), no. 5, 939 - 970 (with Y. Latushkin)

45. The algebraic multiplicity of eigenvalues and the Evans function revisited, in Memorial M. Birman's volume, Mat. Model. Nat. Phenom., 5 (2010) 269 - 292 (with Y. Latushkin)

46. Spectral decomposition of normal operators in Hilbert quaternion bimodules, Scientific Notes of Taurida National University, 19(58) (2006), no. 1, 3-20 (with I. Karpenko, D. Tyshkevich)

47. On an approach to differentiation of functions of a quaternion variable, Scientific Notes of Taurida National University, 17(56) (2004), no. 1, 30-37 (with I. Karpenko, D. Tyshkevich)

48. Thesis: "The Evans function, the Weyl-Titchmarsh function, and the Birman-Schwinger operators", July 2012

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