Cox, Graham; Curran, Mitchell; Latushkin, Yuri; Marangell, Robert Hamiltonian spectral flows, the Maslov index, and the stability of standing waves in the nonlinear Schrödinger equation. (English) Zbl 1526.34064 SIAM J. Math. Anal. 55, No. 5, 4998-5050 (2023). Reviewer: Rakib Efendiev (Baku) MSC: 34L05 34L15 34L40 37K25 34C37 47E05 53D12 PDFBibTeX XMLCite \textit{G. Cox} et al., SIAM J. Math. Anal. 55, No. 5, 4998--5050 (2023; Zbl 1526.34064) Full Text: DOI arXiv
Howard, Peter The Maslov index and spectral counts for linear Hamiltonian systems on \(\mathbb{R}\). (English) Zbl 07729190 J. Dyn. Differ. Equations 35, No. 3, 1947-1991 (2023). Reviewer: Abderrazek Benhassine (Monastir) MSC: 37J51 34B24 53D12 PDFBibTeX XMLCite \textit{P. Howard}, J. Dyn. Differ. Equations 35, No. 3, 1947--1991 (2023; Zbl 07729190) Full Text: DOI arXiv
Sandstede, Björn; Scheel, Arnd Spiral waves: linear and nonlinear theory. (English) Zbl 07689875 Memoirs of the American Mathematical Society 1413. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-6309-0/pbk; 978-1-4704-7483-6/ebook). v, 126 p. (2023). MSC: 35-02 35B36 35B40 37L15 PDFBibTeX XMLCite \textit{B. Sandstede} and \textit{A. Scheel}, Spiral waves: linear and nonlinear theory. Providence, RI: American Mathematical Society (AMS) (2023; Zbl 07689875) Full Text: DOI arXiv
Agrachev, Andrei; Baranzini, Stefano; Beschastnyi, Ivan Index theorems for graph-parametrized optimal control problems. (English) Zbl 1515.49016 Nonlinearity 36, No. 5, 2792-2838 (2023). Reviewer: Claudia Simionescu-Badea (Wien) MSC: 49K30 81Q35 53D12 PDFBibTeX XMLCite \textit{A. Agrachev} et al., Nonlinearity 36, No. 5, 2792--2838 (2023; Zbl 1515.49016) Full Text: DOI arXiv
Latushkin, Yuri; Sukhtaiev, Selim Resolvent expansions for self-adjoint operators via boundary triplets. (English) Zbl 07740286 Bull. Lond. Math. Soc. 54, No. 6, 2469-2491 (2022). Reviewer: Massimo Lanza de Cristoforis (Padova) MSC: 35P05 35B20 47A55 47A75 PDFBibTeX XMLCite \textit{Y. Latushkin} and \textit{S. Sukhtaiev}, Bull. Lond. Math. Soc. 54, No. 6, 2469--2491 (2022; Zbl 07740286) Full Text: DOI arXiv
Howard, Peter Renormalized oscillation theory for regular linear non-Hamiltonian systems. (English) Zbl 1508.34011 Commun. Pure Appl. Anal. 21, No. 12, 4311-4345 (2022). MSC: 34A30 34B09 34B05 34B20 34C10 34L15 34L16 53D12 PDFBibTeX XMLCite \textit{P. Howard}, Commun. Pure Appl. Anal. 21, No. 12, 4311--4345 (2022; Zbl 1508.34011) Full Text: DOI arXiv
Burchell, Timothy J.; Bridges, Thomas J. Symplectic transversality and the Pego-Weinstein theory. (English) Zbl 1504.35422 Adv. Math. 406, Article ID 108524, 58 p. (2022). MSC: 35Q41 35Q51 35C08 37C29 15A66 35B40 53D05 76B25 PDFBibTeX XMLCite \textit{T. J. Burchell} and \textit{T. J. Bridges}, Adv. Math. 406, Article ID 108524, 58 p. (2022; Zbl 1504.35422) Full Text: DOI arXiv
Beck, Margaret; Jaquette, Jonathan Validated spectral stability via conjugate points. (English) Zbl 1494.37046 SIAM J. Appl. Dyn. Syst. 21, No. 1, 366-404 (2022). Reviewer: Svetlin Georgiev (Sofia) MSC: 37L15 35K57 35B35 34B24 37M20 37M21 65G20 PDFBibTeX XMLCite \textit{M. Beck} and \textit{J. Jaquette}, SIAM J. Appl. Dyn. Syst. 21, No. 1, 366--404 (2022; Zbl 1494.37046) Full Text: DOI arXiv
Agrachev, Andrei; Beschastnyi, Ivan Jacobi fields in optimal control: Morse and Maslov indices. (English) Zbl 1476.58011 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 214, Article ID 112608, 47 p. (2022). Reviewer: Dumitru Motreanu (Perpignan) MSC: 58E05 58J30 49K15 53D12 PDFBibTeX XMLCite \textit{A. Agrachev} and \textit{I. Beschastnyi}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 214, Article ID 112608, 47 p. (2022; Zbl 1476.58011) Full Text: DOI arXiv
Howard, Peter Hörmander’s index and oscillation theory. (English) Zbl 1465.37072 J. Math. Anal. Appl. 500, No. 1, Article ID 125076, 38 p. (2021). MSC: 37J46 37J51 53D12 34C10 PDFBibTeX XMLCite \textit{P. Howard}, J. Math. Anal. Appl. 500, No. 1, Article ID 125076, 38 p. (2021; Zbl 1465.37072) Full Text: DOI
Beck, Margaret; Cox, Graham; Jones, Christopher; Latushkin, Yuri; Sukhtayev, Alim A dynamical approach to semilinear elliptic equations. (English) Zbl 1459.35174 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 38, No. 2, 421-450 (2021). Reviewer: Dumitru Motreanu (Perpignan) MSC: 35J61 35A24 34D09 35J25 PDFBibTeX XMLCite \textit{M. Beck} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 38, No. 2, 421--450 (2021; Zbl 1459.35174) Full Text: DOI arXiv
Beck, Margaret; Cox, Graham; Jones, Christopher; Latushkin, Yuri; Sukhtayev, Alim Exponential dichotomies for elliptic PDE on radial domains. (English) Zbl 1459.35175 Dörfler, Willy (ed.) et al., Mathematics of wave phenomena. Selected papers based on the presentations at the conference, Karlsruhe, Germany, July 23–27, 2018. Cham: Birkhäuser. Trends Math., 49-68 (2020). MSC: 35J61 PDFBibTeX XMLCite \textit{M. Beck} et al., in: Mathematics of wave phenomena. Selected papers based on the presentations at the conference, Karlsruhe, Germany, July 23--27, 2018. Cham: Birkhäuser. 49--68 (2020; Zbl 1459.35175) Full Text: DOI arXiv
Latushkin, Yuri; Sukhtaiev, Selim An index theorem for Schrödinger operators on metric graphs. (English) Zbl 1457.58014 Abdul-Rahman, Houssam (ed.) et al., Analytic trends in mathematical physics. Arizona school of analysis and mathematical physics, University of Arizona, Tucson, AZ, USA, March 5–9, 2018. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 741, 105-119 (2020). MSC: 58J30 35R02 PDFBibTeX XMLCite \textit{Y. Latushkin} and \textit{S. Sukhtaiev}, Contemp. Math. 741, 105--119 (2020; Zbl 1457.58014) Full Text: DOI arXiv
Cox, Graham; Marzuola, Jeremy L. A symplectic perspective on constrained eigenvalue problems. (English) Zbl 1408.35106 J. Differ. Equations 266, No. 6, 2924-2952 (2019). Reviewer: Nikhil Savale (Köln) MSC: 35P15 35Q55 35C08 35J91 PDFBibTeX XMLCite \textit{G. Cox} and \textit{J. L. Marzuola}, J. Differ. Equations 266, No. 6, 2924--2952 (2019; Zbl 1408.35106) Full Text: DOI arXiv
Howard, P.; Latushkin, Y.; Sukhtayev, A. The Maslov and Morse indices for system Schrödinger operators on \(\mathbb{R}\). (English) Zbl 1408.53106 Indiana Univ. Math. J. 67, No. 5, 1765-1815 (2018). MSC: 53D12 34L40 PDFBibTeX XMLCite \textit{P. Howard} et al., Indiana Univ. Math. J. 67, No. 5, 1765--1815 (2018; Zbl 1408.53106) Full Text: DOI
Beck, M.; Cox, G.; Jones, C.; Latushkin, Y.; McQuighan, K.; Sukhtayev, A. Instability of pulses in gradient reaction-diffusion systems: a symplectic approach. (English) Zbl 1402.35137 Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 376, No. 2117, Article ID 20170187, 20 p. (2018). MSC: 35K40 35K57 35B35 PDFBibTeX XMLCite \textit{M. Beck} et al., Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 376, No. 2117, Article ID 20170187, 20 p. (2018; Zbl 1402.35137) Full Text: DOI arXiv
Howard, Peter; Jung, Soyeun; Kwon, Bongsuk The Maslov index and spectral counts for linear Hamiltonian systems on \([0, 1]\). (English) Zbl 1404.37064 J. Dyn. Differ. Equations 30, No. 4, 1703-1729 (2018). MSC: 37J05 34L10 PDFBibTeX XMLCite \textit{P. Howard} et al., J. Dyn. Differ. Equations 30, No. 4, 1703--1729 (2018; Zbl 1404.37064) Full Text: DOI
Latushkin, Yuri; Sukhtaiev, Selim; Sukhtayev, Alim The Morse and Maslov indices for Schrödinger operators. (English) Zbl 1407.35073 J. Anal. Math. 135, No. 1, 345-387 (2018). Reviewer: Petar Popivanov (Sofia) MSC: 35J10 47F05 35P05 PDFBibTeX XMLCite \textit{Y. Latushkin} et al., J. Anal. Math. 135, No. 1, 345--387 (2018; Zbl 1407.35073) Full Text: DOI arXiv
Latushkin, Yuri; Sukhtaiev, Selim The Maslov index and the spectra of second order elliptic operators. (English) Zbl 06863449 Adv. Math. 329, 422-486 (2018). MSC: 47-XX 35-XX PDFBibTeX XMLCite \textit{Y. Latushkin} and \textit{S. Sukhtaiev}, Adv. Math. 329, 422--486 (2018; Zbl 06863449) Full Text: DOI arXiv
Howard, P.; Latushkin, Y.; Sukhtayev, A. The Maslov index for Lagrangian pairs on \(\mathbb{R}^{2 n}\). (English) Zbl 1377.35073 J. Math. Anal. Appl. 451, No. 2, 794-821 (2017). MSC: 35J10 53D12 PDFBibTeX XMLCite \textit{P. Howard} et al., J. Math. Anal. Appl. 451, No. 2, 794--821 (2017; Zbl 1377.35073) Full Text: DOI arXiv
Latushkin, Yuri; Sukhtayev, Alim Hadamard-type formulas via the Maslov form. (English) Zbl 1418.34161 J. Evol. Equ. 17, No. 1, 443-472 (2017). MSC: 34L40 34L15 34L20 PDFBibTeX XMLCite \textit{Y. Latushkin} and \textit{A. Sukhtayev}, J. Evol. Equ. 17, No. 1, 443--472 (2017; Zbl 1418.34161) Full Text: DOI arXiv
Jones, Christopher K. R. T.; Latushkin, Yuri; Sukhtaiev, Selim Counting spectrum via the Maslov index for one dimensional \(\theta\)-periodic Schrödinger operators. (English) Zbl 1353.53080 Proc. Am. Math. Soc. 145, No. 1, 363-377 (2017). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 53D12 34L40 37J25 70H12 PDFBibTeX XMLCite \textit{C. K. R. T. Jones} et al., Proc. Am. Math. Soc. 145, No. 1, 363--377 (2017; Zbl 1353.53080) Full Text: DOI arXiv