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Journal articles on the topic 'First-order differential operators'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Ismailov, Z. I., and P. Ipek Al. "BOUNDEDLY SOLVABLE NEUTRAL TYPE DELAY DIFFERENTIAL OPERATORS OF THE FIRST ORDER." Eurasian Mathematical Journal 10, no. 3 (2019): 20–27. http://dx.doi.org/10.32523/2077-9879-2019-10-3-20-27.

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2

Ueno, Kazushige. "On pseudoelliptic systems of first order differential equations." Nagoya Mathematical Journal 108 (December 1987): 15–51. http://dx.doi.org/10.1017/s0027763000002634.

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In the study of elliptic differential operators of second order, we found that the automorphism pseudogroups are of finite type ([4]). However this fact takes a complete change in elliptic differential operators of first order.So as to make the objects which can be dealt with clear, we introduce the concept of pseudoellipticity of first order differential operators (Definition 1.1), which is naturally satisfied by first order elliptic differential operators.

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3

Ipek Al, P., and Z. I. Ismailov. "First Order Selfadjoint Differential Operators with Involution." Lobachevskii Journal of Mathematics 42, no. 3 (March 2021): 496–501. http://dx.doi.org/10.1134/s1995080221030045.

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4

Gatse, Servais Cyr. "Some Properties of First Order Differential Operators." Advances in Pure Mathematics 09, no. 11 (2019): 934–43. http://dx.doi.org/10.4236/apm.2019.911046.

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5

Ismailov, Z. I., B. O. Guler, and P. Ipek. "Solvability of first order functional differential operators." Journal of Mathematical Chemistry 53, no. 9 (July 28, 2015): 2065–77. http://dx.doi.org/10.1007/s10910-015-0534-2.

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6

Ismailov, Zameddin I. "Multipoint normal differential operators of first order." Opuscula Mathematica 29, no. 4 (2009): 399. http://dx.doi.org/10.7494/opmath.2009.29.4.399.

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7

Pembe; ISMAILOV, İPEK. "SELFADJOINT SINGULAR DIFFERENTIAL OPERATORS FOR FIRST ORDER." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 67, no. 2 (2018): 156–64. http://dx.doi.org/10.1501/commua1_0000000870.

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8

Chernyshov, M. K. "Invertibility of first-order linear differential operators." Mathematical Notes 64, no. 5 (November 1998): 688–93. http://dx.doi.org/10.1007/bf02316297.

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9

ÖZTÜRK MERT, Rukiye, Bülent YILMAZ, and Zameddin I. Ismailov. "Multipoint selfadjoint quasi-differential operators for first order." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 68, no. 1 (April 11, 2018): 964–72. http://dx.doi.org/10.31801/cfsuasmas.501414.

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10

İpek, Pembe, and Zameddin İsmailov. "Boundedly solvable degenerate differential operators for first order." Universal Journal of Mathematics and Applications 1, no. 1 (March 15, 2018): 68–73. http://dx.doi.org/10.32323/ujma.387330.

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11

Cialdea, A., and V. Maz’ya. "The -dissipativity of first order partial differential operators." Complex Variables and Elliptic Equations 63, no. 7-8 (June 20, 2017): 945–60. http://dx.doi.org/10.1080/17476933.2017.1321638.

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12

Sabadini, Irene, and Daniele C. Struppa. "First Order Differential Operators in Real Dimension Eight." Complex Variables, Theory and Application: An International Journal 47, no. 10 (October 2002): 953–68. http://dx.doi.org/10.1080/02781070290034584.

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13

Draisma, Jan. "Constructing Lie algebras of first order differential operators." Journal of Symbolic Computation 36, no. 5 (November 2003): 685–98. http://dx.doi.org/10.1016/s0747-7171(03)00061-0.

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14

Johnson, Kenneth D., Adam Korányi, and H. Martin Reimann. "Equivariant first order differential operators for parabolic geometries." Indagationes Mathematicae 14, no. 3-4 (December 2003): 385–93. http://dx.doi.org/10.1016/s0019-3577(03)90053-x.

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15

Chung, Dong Myung, and Tae Su Chung. "First order differential operators in white noise analysis." Proceedings of the American Mathematical Society 126, no. 8 (1998): 2369–76. http://dx.doi.org/10.1090/s0002-9939-98-04323-8.

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16

Benammar, M. "Classification of regularly solvable first-order differential operators." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 120, no. 1-2 (1992): 165–78. http://dx.doi.org/10.1017/s0308210500015067.

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SynopsisIn this article the expression τφ: = pφ + qφ with complex-valued coefficients is considered. We are particularly concerned with this expression when it is not formally symmetric, i.e., τ ≠ τ+, where τ+ is the formal adjoint of τ, and especially with the operators which are regularly solvable with respect to the minimal operators generated by τ and τ+ in the sense of W. D. Evans in [3]. This article is divided into five sections: Section 1 is an introduction, Section 2 is a brief study of the regular problem, in Section 3, some preliminary results in the singular case are displayed in Section 4, the joint field of regularity in the singular case is investigated and in Section 5, we discuss the case when .

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17

ÖZTÜRK MERT, Rukiye, Bülent YILMAZ, and Zameddin I. İSMAİLOV. "First order self-adjoint multipoint quasi-differential operators." TURKISH JOURNAL OF MATHEMATICS 42, no. 4 (July 24, 2018): 2071–79. http://dx.doi.org/10.3906/mat-1803-136.

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18

Ismailov, Zameddin I., and Pembe Ipek Al. "Selfadjoint Singular Quasi-Differential Operators of First Order." Hittite Journal of Science & Engineering 6, no. 1 (2019): 31–35. http://dx.doi.org/10.17350/hjse19030000130.

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19

Yurko, V. A. "Inverse problems for first-order integro-differential operators." Mathematical Notes 100, no. 5-6 (November 2016): 876–82. http://dx.doi.org/10.1134/s0001434616110286.

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20

Shirokov, I. V. "Constructing lie algebras of first-order differential operators." Russian Physics Journal 40, no. 6 (June 1997): 525–30. http://dx.doi.org/10.1007/bf02766382.

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21

Ismailov, Z. I. "Compact inverses of first-order normal differential operators." Journal of Mathematical Analysis and Applications 320, no. 1 (August 2006): 266–78. http://dx.doi.org/10.1016/j.jmaa.2005.06.090.

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22

Vasilevskii, K. V., and F. E. Lomovtsev. "First-order differential-operator equation with variable domains of piecewise smooth operators." Differential Equations 47, no. 2 (February 2011): 244–53. http://dx.doi.org/10.1134/s0012266111020108.

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23

Ipek Al, P., and Ü. Akbaba. "On the Compactly Solvable Differential Operators for First Order." Lobachevskii Journal of Mathematics 41, no. 6 (June 2020): 1078–86. http://dx.doi.org/10.1134/s1995080220060116.

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24

Ismailov, Z. I., and M. Erol. "Normal differential operators of first-order with smooth coefficients." Rocky Mountain Journal of Mathematics 42, no. 2 (April 2012): 633–42. http://dx.doi.org/10.1216/rmj-2012-42-2-633.

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25

Ismailov, Z. I., and P. Ipek. "Spectrums of Solvable Pantograph Differential-Operators for First Order." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/837565.

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By using the methods of operator theory, all solvable extensions of minimal operator generated by first order pantograph-type delay differential-operator expression in the Hilbert space of vector-functions on finite interval have been considered. As a result, the exact formula for the spectrums of these extensions is presented. Applications of obtained results to the concrete models are illustrated.

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26

Anghel, N. "Fredholmness vs. Spectral Discreteness for first-order differential operators." Proceedings of the American Mathematical Society 144, no. 2 (June 26, 2015): 693–701. http://dx.doi.org/10.1090/proc12741.

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27

Ulmet, Marlene Gabriele. "Properties of Semigroups Generated by First Order Differential Operators." Results in Mathematics 22, no. 3-4 (November 1992): 821–32. http://dx.doi.org/10.1007/bf03323126.

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28

SERTBAŞ, Meltem, and Fatih YILMAZ. "Degenerate maximal hyponormal differential operators for the first order." TURKISH JOURNAL OF MATHEMATICS 43, no. 1 (January 18, 2019): 126–31. http://dx.doi.org/10.3906/mat-1805-13.

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29

Fegan, H. D., and B. Steer. "First order differential operators on a locally symmetric space." Pacific Journal of Mathematics 194, no. 1 (May 1, 2000): 83–96. http://dx.doi.org/10.2140/pjm.2000.194.83.

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30

Fegan, H. D., and B. Steer. "First Order Operators on Manifolds With a Group Action." Canadian Journal of Mathematics 48, no. 4 (August 1, 1996): 758–76. http://dx.doi.org/10.4153/cjm-1996-039-6.

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AbstractWe investigate questions of spectral symmetry for certain first order differential operators acting on sections of bundles over manifolds which have a group action. We show that if the manifold is in fact a group we have simple spectral symmetry for all homogeneous operators. Furthermore if the manifold is not necessarily a group but has a compact Lie group of rank 2 or greater acting on it by isometries with discrete isotropy groups, and let D be a split invariant elliptic first order differential operator, then D has equivariant spectral symmetry.

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31

Son, Le Hung, and W. Tutschke. "First Order Differential Operators Associated to the Cauchy—Riemann Operator in the Plane." Complex Variables, Theory and Application: An International Journal 48, no. 9 (January 2003): 797–801. http://dx.doi.org/10.1080/02781077.2003.10807170.

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32

Elizarraraz, David, and Luis Verde-Star. "Similar Operators and a Functional Calculus for the First-Order Linear Differential Operator." Advances in Applied Mathematics 22, no. 1 (January 1999): 29–47. http://dx.doi.org/10.1006/aama.1998.0617.

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33

Yankov, Kaloyan. "PHASE BEHAVIOUR OF FIRST - ORDER SYSTEMS." Applied Researches in Technics, Technologies and Education 16, no. 2 (2018): 131–37. http://dx.doi.org/10.15547/artte.2018.02.008.

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The phase-plane method gives possibility to study the stability of systems described by linear and nonlinear differential equations. The article is devoted to the capabilities of MathCad for analysis of first order differential equations. An algorithm is proposed and Mathcad's specific operators for the construction and analysis of phase trajectories are described. Approaches for calculation of equilibrium points and determination the type of bifurcation in function of parameter are described. The proposed algorithm is applied to the dose-response curve of the antibiotic tubazid.

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34

Felix, Rainer. "Differential operators of the first order with degenerate principal symbols." Banach Center Publications 27, no. 1 (1992): 147–61. http://dx.doi.org/10.4064/-27-1-147-161.

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35

Garkavenko, G., and N. Uskova. "Spectral analysis of one class perturbed first order differential operators." Journal of Physics: Conference Series 1902, no. 1 (May 1, 2021): 012035. http://dx.doi.org/10.1088/1742-6596/1902/1/012035.

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36

Bär, Christian, and Lashi Bandara. "Boundary value problems for general first-order elliptic differential operators." Journal of Functional Analysis 282, no. 12 (June 2022): 109445. http://dx.doi.org/10.1016/j.jfa.2022.109445.

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37

İPEK AL, Pembe. "Spectral analysis of some classes first-order normal differential operators." TURKISH JOURNAL OF MATHEMATICS 43, no. 5 (September 28, 2019): 2308–26. http://dx.doi.org/10.3906/mat-1902-91.

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38

Ballmann, Werner, and Christian Bär. "Boundary value problems for elliptic differential operators of first order." Surveys in Differential Geometry 17, no. 1 (2012): 1–78. http://dx.doi.org/10.4310/sdg.2012.v17.n1.a1.

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39

dos Santos Filho, José R., and Maurício Fronza da Silva. "Global solvability for first order real linear partial differential operators." Journal of Differential Equations 247, no. 10 (November 2009): 2688–704. http://dx.doi.org/10.1016/j.jde.2009.08.017.

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40

Korányi, A., and H. M. Reimann. "Equivariant first order differential operators on boundaries of symmetric spaces." Inventiones mathematicae 139, no. 2 (February 2000): 371–90. http://dx.doi.org/10.1007/s002229900030.

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41

El Khattabi, N., M. Frigon, and N. Ayyadi. "Multiple solutions of problems with nonlinear first-order differential operators." Journal of Fixed Point Theory and Applications 17, no. 1 (March 2015): 23–42. http://dx.doi.org/10.1007/s11784-015-0230-7.

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42

Loya, Paul, and Sergiu Moroianu. "Singularities of the eta function of first order differential operators." Analele Universitatii "Ovidius" Constanta - Seria Matematica 20, no. 2 (June 1, 2012): 59–70. http://dx.doi.org/10.2478/v10309-012-0040-5.

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Abstract We report on a particular case of the paper [7], joint with Raphaël Ponge, showing that generically, the eta function of a first-order differential operator over a closed manifold of dimension n has first-order poles at all positive integers of the form n - 1; n - 3; n - 5;. . . .

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43

Rao, Aribindi Satyanarayan. "On first-order differential operators with Bohr-Neugebauer type property." International Journal of Mathematics and Mathematical Sciences 12, no. 3 (1989): 473–76. http://dx.doi.org/10.1155/s0161171289000608.

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We consider a differential equationddtu(t)-Bu(t)=f(t), where the functions u and f map the real line into a Banach space X and B: X→X is a bounded linear operator. Assuming that any Stepanov-bounded solution u is Stepanov almost-periodic when f is Bochner almost-periodic, we establish that any Stepanov-bounded solution u is Bochner almost-periodic when f is Stepanov almost-periodic. Some examples are given in which the operatorddt-B is shown to satisfy our assumption.

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44

Chvalina, Jan, and Šárka Hošková-Mayerová. "On Certain Proximities and Preorderings on the Transposition Hypergroups of Linear First-Order Partial Differential Operators." Analele Universitatii "Ovidius" Constanta - Seria Matematica 22, no. 1 (December 10, 2014): 85–103. http://dx.doi.org/10.2478/auom-2014-0008.

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AbstractThe contribution aims to create hypergroups of linear first-order partial differential operators with proximities, one of which creates a tolerance semigroup on the power set of the mentioned differential operators. Constructions of investigated hypergroups are based on the so called “Ends-Lemma” applied on ordered groups of differnetial operators. Moreover, there is also obtained a regularly preordered transpositions hypergroup of considered partial differntial operators.

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45

Tutschke, Wolfgang. "First-order differential operators in the three-dimensional euclidean space being associated to the differential operator rot." Complex Variables, Theory and Application: An International Journal 7, no. 4 (January 1987): 349–55. http://dx.doi.org/10.1080/17476938708814210.

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46

Krishtal, I. A., and N. B. Uskova. "Spectral properties of first-order differential operators with an involution and groups of operators." Sibirskie Elektronnye Matematicheskie Izvestiya 16 (August 16, 2019): 1091–132. http://dx.doi.org/10.33048/semi.2019.16.076.

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47

dos Santos Filho, José R., and Maurício Fronza da Silva. "Global solvability for first order real linear partial differential operators III." Journal of Differential Equations 286 (June 2021): 731–50. http://dx.doi.org/10.1016/j.jde.2021.03.025.

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48

Öztürk Mert, R. "Representation of All Maximally Dissipative Multipoint Differential Operators for First Order." Lobachevskii Journal of Mathematics 41, no. 9 (September 2020): 1854–63. http://dx.doi.org/10.1134/s199508022009019x.

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49

dos Santos Filho, José R., and Maurício Fronza da Silva. "Global solvability for first order real linear partial differential operators II." Journal of Differential Equations 253, no. 3 (August 2012): 933–50. http://dx.doi.org/10.1016/j.jde.2012.04.019.

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50

Eelbode, D. "Fundamental solutions for first order Spin (1, m )-invariant differential operators." Archiv der Mathematik 82, no. 1 (January 1, 2004): 51–60. http://dx.doi.org/10.1007/s00013-003-0108-6.

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