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An integral representation of the determinant of a matrix and its applications
1.  Department of Mathematics, Kennesaw State University, 1000 Chastain Rd, P.O. Box 1204, Kennesaw, GA 30144, United States, United States 
[1] 
Pedro Teixeira. DacorognaMoser theorem on the Jacobian determinant equation with control of support. Discrete and Continuous Dynamical Systems, 2017, 37 (7) : 40714089. doi: 10.3934/dcds.2017173 
[2] 
Indranil Biswas, Georg Schumacher, Lin Weng. Deligne pairing and determinant bundle. Electronic Research Announcements, 2011, 18: 9196. doi: 10.3934/era.2011.18.91 
[3] 
Yves Capdeboscq, Shaun Chen Yang Ong. Quantitative jacobian determinant bounds for the conductivity equation in high contrast composite media. Discrete and Continuous Dynamical Systems  B, 2020, 25 (10) : 38573887. doi: 10.3934/dcdsb.2020228 
[4] 
Simon Scott. Relative zeta determinants and the geometry of the determinant line bundle. Electronic Research Announcements, 2001, 7: 816. 
[5] 
Zhenjie Li, Ze Cheng, Dongsheng Li. The Liouville type theorem and local regularity results for nonlinear differential and integral systems. Communications on Pure and Applied Analysis, 2015, 14 (2) : 565576. doi: 10.3934/cpaa.2015.14.565 
[6] 
Farid Tari. Geometric properties of the integral curves of an implicit differential equation. Discrete and Continuous Dynamical Systems, 2007, 17 (2) : 349364. doi: 10.3934/dcds.2007.17.349 
[7] 
Changpin Li, Zhiqiang Li. Asymptotic behaviors of solution to partial differential equation with Caputo–Hadamard derivative and fractional Laplacian: Hyperbolic case. Discrete and Continuous Dynamical Systems  S, 2021, 14 (10) : 36593683. doi: 10.3934/dcdss.2021023 
[8] 
Kanghui Guo and Demetrio Labate. Sparse shearlet representation of Fourier integral operators. Electronic Research Announcements, 2007, 14: 719. doi: 10.3934/era.2007.14.7 
[9] 
Giuseppe Da Prato. An integral inequality for the invariant measure of some finite dimensional stochastic differential equation. Discrete and Continuous Dynamical Systems  B, 2016, 21 (9) : 30153027. doi: 10.3934/dcdsb.2016085 
[10] 
Richard A. Norton, G. R. W. Quispel. Discrete gradient methods for preserving a first integral of an ordinary differential equation. Discrete and Continuous Dynamical Systems, 2014, 34 (3) : 11471170. doi: 10.3934/dcds.2014.34.1147 
[11] 
Dezhong Chen, Li Ma. A Liouville type Theorem for an integral system. Communications on Pure and Applied Analysis, 2006, 5 (4) : 855859. doi: 10.3934/cpaa.2006.5.855 
[12] 
Michael Dellnitz, Mirko HesselVon Molo, Adrian Ziessler. On the computation of attractors for delay differential equations. Journal of Computational Dynamics, 2016, 3 (1) : 93112. doi: 10.3934/jcd.2016005 
[13] 
Pavel Krejčí, Harbir Lamba, Sergey Melnik, Dmitrii Rachinskii. Kurzweil integral representation of interacting PrandtlIshlinskii operators. Discrete and Continuous Dynamical Systems  B, 2015, 20 (9) : 29492965. doi: 10.3934/dcdsb.2015.20.2949 
[14] 
David M. McClendon. An AmbroseKakutani representation theorem for countableto1 semiflows. Discrete and Continuous Dynamical Systems  S, 2009, 2 (2) : 251268. doi: 10.3934/dcdss.2009.2.251 
[15] 
Jingbo Dou, Ye Li. Liouville theorem for an integral system on the upper half space. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 155171. doi: 10.3934/dcds.2015.35.155 
[16] 
Eitan Tadmor, Prashant Athavale. Multiscale image representation using novel integrodifferential equations. Inverse Problems and Imaging, 2009, 3 (4) : 693710. doi: 10.3934/ipi.2009.3.693 
[17] 
Weiwei Zhao, Jinge Yang, Sining Zheng. Liouville type theorem to an integral system in the halfspace. Communications on Pure and Applied Analysis, 2014, 13 (2) : 511525. doi: 10.3934/cpaa.2014.13.511 
[18] 
Robert Baier, Lars Grüne, Sigurđur Freyr Hafstein. Linear programming based Lyapunov function computation for differential inclusions. Discrete and Continuous Dynamical Systems  B, 2012, 17 (1) : 3356. doi: 10.3934/dcdsb.2012.17.33 
[19] 
Wenxiong Chen, Congming Li, Biao Ou. Qualitative properties of solutions for an integral equation. Discrete and Continuous Dynamical Systems, 2005, 12 (2) : 347354. doi: 10.3934/dcds.2005.12.347 
[20] 
Nguyen Dinh Cong, Doan Thai Son. On integral separation of bounded linear random differential equations. Discrete and Continuous Dynamical Systems  S, 2016, 9 (4) : 9951007. doi: 10.3934/dcdss.2016038 
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