Borisov, D. I.; Golovina, A. M. On finitely many resonances emerging under distant perturbations in multi-dimensional cylinders. (English) Zbl 1458.81018 J. Math. Anal. Appl. 496, No. 2, Article ID 124809, 28 p. (2021). MSC: 81Q05 35B34 35B40 35J10 35B20 35P05 47A75 PDFBibTeX XMLCite \textit{D. I. Borisov} and \textit{A. M. Golovina}, J. Math. Anal. Appl. 496, No. 2, Article ID 124809, 28 p. (2021; Zbl 1458.81018) Full Text: DOI arXiv
Borisov, Denis Ivanovich; Konyrkulzhaeva, Maral Nurlanovna On infinite system of resonance and eigenvalues with exponential asymptotics generated by distant perturbations. (Russian. English translation) Zbl 1474.34597 Ufim. Mat. Zh. 12, No. 4, 3-19 (2020); translation in Ufa Math. J., No. 4, 3-18 (2020). MSC: 34L05 34L40 34L15 PDFBibTeX XMLCite \textit{D. I. Borisov} and \textit{M. N. Konyrkulzhaeva}, Ufim. Mat. Zh. 12, No. 4, 3--19 (2020; Zbl 1474.34597); translation in Ufa Math. J., No. 4, 3--18 (2020) Full Text: DOI MNR
Borisov, D. I.; Mukhametrakhimova, A. I. On a model graph with a loop and small edges. Holomorphy property of resolvent. (English. Russian original) Zbl 1458.34059 J. Math. Sci., New York 251, No. 5, 573-601 (2020); translation from Probl. Mat. Anal. 106, 17-41 (2020). Reviewer: Vjacheslav Yurko (Saratov) MSC: 34B45 34L40 47E05 PDFBibTeX XMLCite \textit{D. I. Borisov} and \textit{A. I. Mukhametrakhimova}, J. Math. Sci., New York 251, No. 5, 573--601 (2020; Zbl 1458.34059); translation from Probl. Mat. Anal. 106, 17--41 (2020) Full Text: DOI
Borisov, D.; Sultanov, O. Asymptotic analysis of mean exit time for dynamical systems with a single well potential. (English) Zbl 1441.35020 J. Differ. Equations 269, No. 8, 78-116 (2020). MSC: 35B25 35C20 35J25 PDFBibTeX XMLCite \textit{D. Borisov} and \textit{O. Sultanov}, J. Differ. Equations 269, No. 8, 78--116 (2020; Zbl 1441.35020) Full Text: DOI arXiv
Borisov, Denis Ivanovich; Konyrkulzhaeva, Maral Nurlanovna Simplest graphs with small edges: asymptotics for resolvents and holomorphic dependence of spectrum. (Russian. English summary) Zbl 1463.34127 Ufim. Mat. Zh. 11, No. 2, 56-71 (2019); translation in Ufa Math. J. 11, No. 2, 56-70 (2019). MSC: 34B45 34L40 34L15 PDFBibTeX XMLCite \textit{D. I. Borisov} and \textit{M. N. Konyrkulzhaeva}, Ufim. Mat. Zh. 11, No. 2, 56--71 (2019; Zbl 1463.34127); translation in Ufa Math. J. 11, No. 2, 56--70 (2019) Full Text: DOI MNR
Borisov, D. I.; Konyrkulzhaeva, M. N. Perturbation of threshold of the essential spectrum of the Schrödinger operator on the simplest graph with a small edge. (English. Russian original) Zbl 1426.34039 J. Math. Sci., New York 239, No. 3, 248-267 (2019); translation from Probl. Mat. Anal. 97, 15-30 (2019). Reviewer: Jiři Lipovský (Hradec Kralove) MSC: 34B45 34L40 34L05 34E10 34L15 PDFBibTeX XMLCite \textit{D. I. Borisov} and \textit{M. N. Konyrkulzhaeva}, J. Math. Sci., New York 239, No. 3, 248--267 (2019; Zbl 1426.34039); translation from Probl. Mat. Anal. 97, 15--30 (2019) Full Text: DOI
Borisov, Denis; Freitas, Pedro The spectrum of geodesic balls on spherically symmetric manifolds. (English) Zbl 1380.53047 Commun. Anal. Geom. 25, No. 3, 507-544 (2017). MSC: 53C21 58J50 53C40 35P15 58C40 PDFBibTeX XMLCite \textit{D. Borisov} and \textit{P. Freitas}, Commun. Anal. Geom. 25, No. 3, 507--544 (2017; Zbl 1380.53047) Full Text: DOI arXiv
Borisov, Denis I.; Znojil, Miloslav On eigenvalues of a \(\mathcal{PT}\)-symmetric operator in a thin layer. (English. Russian original) Zbl 1371.35178 Sb. Math. 208, No. 2, 173-199 (2017); translation from Mat. Sb. 208, No. 2, 3-30 (2017). MSC: 35P15 35P20 47F05 PDFBibTeX XMLCite \textit{D. I. Borisov} and \textit{M. Znojil}, Sb. Math. 208, No. 2, 173--199 (2017; Zbl 1371.35178); translation from Mat. Sb. 208, No. 2, 3--30 (2017) Full Text: DOI
Borisov, D. I. On a \(\mathcal{PT}\)-symmetric waveguide with a pair of small holes. (English. Russian original) Zbl 1321.47166 Proc. Steklov Inst. Math. 281, Suppl. 1, S5-S21 (2013); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 18, No. 2, 22-37 (2012). Reviewer: Vladimir N. Karpushkin (Moskva) MSC: 47N50 81Q37 PDFBibTeX XMLCite \textit{D. I. Borisov}, Proc. Steklov Inst. Math. 281, S5--S21 (2013; Zbl 1321.47166); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 18, No. 2, 22--37 (2012) Full Text: DOI
Borisov, Denis; Freitas, Pedro Asymptotics of Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin domains in \(\mathbb R^d\). (English) Zbl 1180.35397 J. Funct. Anal. 258, No. 3, 893-912 (2010). MSC: 35P20 35J05 35C20 PDFBibTeX XMLCite \textit{D. Borisov} and \textit{P. Freitas}, J. Funct. Anal. 258, No. 3, 893--912 (2010; Zbl 1180.35397) Full Text: DOI arXiv
Borisov, Denis; Freitas, Pedro Eigenvalue asymptotics, inverse problems and a trace formula for the linear damped wave equation. (English) Zbl 1181.35151 J. Differ. Equations 247, No. 11, 3028-3039 (2009). MSC: 35P15 35L05 PDFBibTeX XMLCite \textit{D. Borisov} and \textit{P. Freitas}, J. Differ. Equations 247, No. 11, 3028--3039 (2009; Zbl 1181.35151) Full Text: DOI arXiv
Borisov, Denis; Freitas, Pedro Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin planar domains. (English) Zbl 1168.35401 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26, No. 2, 547-560 (2009). MSC: 35P10 35P15 35J05 PDFBibTeX XMLCite \textit{D. Borisov} and \textit{P. Freitas}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26, No. 2, 547--560 (2009; Zbl 1168.35401) Full Text: DOI arXiv EuDML
Borisov, Denis; Krejčiřík, David \(\mathcal {PT}\)-symmetric waveguides. (English) Zbl 1178.35141 Integral Equations Oper. Theory 62, No. 4, 489-515 (2008). Reviewer: Stepan Agop Tersian (Rousse) MSC: 35J05 47B44 35P15 47F05 PDFBibTeX XMLCite \textit{D. Borisov} and \textit{D. Krejčiřík}, Integral Equations Oper. Theory 62, No. 4, 489--515 (2008; Zbl 1178.35141) Full Text: DOI arXiv
Borisov, D. I.; Gadyl’shin, R. R. On the spectrum of a periodic operator with a small localized perturbation. (English. Russian original) Zbl 1169.34056 Izv. Math. 72, No. 4, 659-688 (2008); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 72, No. 4, 37-66 (2008). Reviewer: Amin Boumenir (Carrollton) MSC: 34L05 47E05 34E10 34L40 47A10 PDFBibTeX XMLCite \textit{D. I. Borisov} and \textit{R. R. Gadyl'shin}, Izv. Math. 72, No. 4, 659--688 (2008; Zbl 1169.34056); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 72, No. 4, 37--66 (2008) Full Text: DOI arXiv
Borisov, Denis Asymptotic behaviour of the spectrum of a waveguide with distant perturbations. (English) Zbl 1185.35155 Math. Phys. Anal. Geom. 10, No. 2, 155-196 (2007). MSC: 35P20 81Q10 PDFBibTeX XMLCite \textit{D. Borisov}, Math. Phys. Anal. Geom. 10, No. 2, 155--196 (2007; Zbl 1185.35155) Full Text: DOI arXiv
Borisov, D. I. Two-parameter asymptotics in a boundary value problem for the Laplacian. (English. Russian original) Zbl 1140.35544 Math. Notes 70, No. 4, 471-485 (2001); translation from Mat. Zametki 70, No. 4, 520-534 (2001). MSC: 35P05 35J05 PDFBibTeX XMLCite \textit{D. I. Borisov}, Math. Notes 70, No. 4, 471--485 (2001; Zbl 1140.35544); translation from Mat. Zametki 70, No. 4, 520--534 (2001) Full Text: DOI