Institute of Mathematics

References:
[1] M. Ashordia: Lyapunov stability of systems of linear generalized ordinary differential equations. Comput. Math. Appl. 50 (2005), 957-982. DOI 10.1016/j.camwa.2004.04.041 | MR 2165650 | Zbl 1090.34043
[2] D. Bainov, P. Simeonov: Impulsive Differential Equations: Periodic Solutions and Applications. Pitman Monographs and Surveys in Pure and Applied Mathematics 66. John Wiley & Sons, New York (1993). DOI 10.1201/9780203751206 | MR 1266625 | Zbl 0815.34001
[3] R. G. Bartle: A general bilinear vector integral. Stud. Math. 15 (1956), 337-352. DOI 10.4064/sm-15-3-337-352 | MR 0080721 | Zbl 0070.28102
[4] N. V. Bedyuk, O. L. Yablonskii: Nonautonomous differential equations in the algebra of new generalized functions. Differ. Equ. 45 (2009), 6-17. DOI 10.1134/S0012266109010029 | MR 2597089 | Zbl 1177.34010
[5] N. Bedziuk, A. Yablonski: Solutions of nonlinear differential equations. NoDEA, Nonlinear Differ. Equ. Appl. 17 (2010), 249-270. DOI 10.1007/s00030-009-0052-7 | MR 2639154 | Zbl 1196.34021
[6] M. Benchohra, J. Henderson, S. Ntouyas: Impulsive Differential Equations and Inclusions. Contemporary Mathematics and Its Applications 2. Hindawi, New York (2006). DOI 10.1155/9789775945501 | MR 2322133 | Zbl 1130.34003
[7] E. M. Bonotto, M. Federson, J. G. Mesquita (eds.): Generalized Ordinary Differential Equations in Abstract Spaces and Applications. John Wiley & Sons, Hoboken (2021). DOI 10.1002/9781119655022 | MR 4485099 | Zbl 1475.34001
[8] B. Brogliato: Nonsmooth Mechanics: Models, Dynamics and Control. Communications and Control Engineering. Springer, Cham (2016). DOI 10.1007/978-3-319-28664-8 | MR 3467591 | Zbl 1333.74002
[9] F. E. Burk: A Garden of Integrals. The Dolciani Mathematical Expositions 31. Mathematical Association of America, Washington (2007). DOI 10.7135/UPO9781614442097 | MR 2311537 | Zbl 1127.26300
[10] G. Buttazzo, M. Giaquinta, S. Hildebrandt: One-Dimensional Variational Problems: An Introduction. Oxford Lecture Series in Mathematics and its Applications 15. Clarendon Press, Oxford (1998). MR 1694383 | Zbl 0915.49001
[11] Y. Cao, J. Sun: Existence of solutions for semilinear measure driven equations. J. Math. Anal. Appl. 425 (2015), 621-631. DOI 10.1016/j.jmaa.2014.12.042 | MR 3303881 | Zbl 1304.34015
[12] M. Carter, B. van Brunt: The Lebesgue-Stieltjes Integral: A Practical Introduction. Undergraduate Texts in Mathematics. Springer, New York (2000). DOI 10.1007/978-1-4612-1174-7 | MR 1759133 | Zbl 0948.28001
[13] M. Cichoń, B. R. Satco: Measure differential inclusions - between continuous and discrete. Adv. Difference Equ. 2014 (2014), Article ID 56, 18 pages. DOI 10.1186/1687-1847-2014-56 | MR 3348625 | Zbl 1350.49014
[14] E. A. Coddington, N. Levinson: Theory of Ordinary Differential Equations. McGraw-Hill, New York (1955). MR 0069338 | Zbl 0064.33002
[15] P. C. Das, R. R. Sharma: Existence and stability of measure differential equations. Czech. Math. J. 22 (1972), 145-158. DOI 10.21136/CMJ.1972.101082 | MR 0304815 | Zbl 0241.34070
[16] P. C. Das, R. R. Sharma: Some Stieltjes integral inequalities. J. Math. Anal. Appl. 73 (1980), 423-433. DOI 10.1016/0022-247X(80)90288-7 | MR 0563993 | Zbl 0432.26008
[17] J. Diestel, J. J. Uhl, Jr.: Vector Measures. Mathematical Surveys 15. AMS, Providence (1977). DOI 10.1090/surv/015 | MR 0453964 | Zbl 0369.46039
[18] L. C. Evans, R. F. Gariepy: Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics. CRC Press, Boca Raton (1992). DOI 10.1201/b18333 | MR 1158660 | Zbl 0804.28001
[19] A. F. Filippov: Differential Equations with Discontinuous Righthand Sides: Control Systems. Mathematics and Its Applications: Soviet Series 18. Kluwer Academic, Dordrecht (1988). DOI 10.1007/978-94-015-7793-9 | MR 1028776 | Zbl 0664.34001
[20] G. B. Folland: Real Analysis: Modern Techniques and Their Applications. Pure and Applied Mathematics. John Wiley & Sons, New York (1999). MR 1681462 | Zbl 0924.28001
[21] E. Hewitt, K. Stromberg: Real and Abstract Analysis: A Modern Treatment of the Theory of Functions of a Real Variable. Graduate Texts in Mathematics 25. Springer, New York (1975). DOI 10.1007/978-3-662-29794-0 | MR 0367121 | Zbl 0307.28001
[22] M. A. Khamsi, W. M. Kozlowski: Fixed Point Theory in Modular Function Spaces. Birkhäuser/Springer, Cham (2015). DOI 10.1007/978-3-319-14051-3 | MR 3329163 | Zbl 1318.47002
[23] S. Kumar, R. P. Agarwal: Existence of solution for non-autonomous semilinear measure driven equations. Differ. Equ. Appl. 12 (2020), 313-322. DOI 10.7153/dea-2020-12-20 | MR 4155961 | Zbl 1474.34407
[24] D. S. Kurtz, C. W. Swartz: Theories of Integration: The Integrals of Riemann, Lebesgue, Henstock-Kurzweil, and McShane. Series in Real Analysis 9. World Scientific, River Edge (2004). DOI 10.1142/5538 | MR 2081182 | Zbl 1072.26005
[25] J. Kurzweil: Henstock-Kurzweil Integration: Its Relation to Topological Vector Spaces. Series in Real Analysis 7. World Scientific, Singapore (2000). DOI 10.1142/4333 | MR 1763305 | Zbl 0954.28001
[26] J. Kurzweil: Integration between the Lebesgue Integral and the Henstock-Kurzweil Integral: Its Relation to Local Convex Vector Spaces. Series in Real Analysis 8. World Scientific, Singapore (2002). DOI 10.1142/5005 | MR 1908744 | Zbl 1018.26005
[27] J. Kurzweil: Generalized Ordinary Differential Equations: Not Absolutely Continuous Solutions. Series in Real Analysis 11. World Scientific, Hackensack (2012). DOI 10.1142/7907 | MR 2906899 | Zbl 1248.34001
[28] V. Lakshmikantham, D. D. Bainov, P. S. Simeonov: Theory of Impulsive Differential Equations. Series in Modern Applied Mathematics 6. World Scientific, Singapore (1989). DOI 10.1142/0906 | MR 1082551 | Zbl 0719.34002
[29] G. A. Leonov, H. Nijmeijer, A., A. Fradkov (eds.): Dynamics and Control of Hybrid Mechanical Systems. World Scientific Series on Nonlinear Science. Series B: Special Theme Issues and Proceedings 14. World Scientific, Hackensack (2010). DOI 10.1142/7421 | Zbl 1183.93003
[30] C. D. Meyer: Matrix Analysis and Applied Linear Algebra. SIAM, Philadelphia (2000). MR 1777382 | Zbl 0962.15001
[31] J. J. Moreau: Unilateral contact and dry friction in finite freedom dynamics. Nonsmooth Mechanics and Applications International Centre for Mechanical Sciences. Springer, Wien (1988), 1-82. DOI 10.1007/978-3-7091-2624-0_1 | Zbl 0703.73070
[32] S. G. Pandit, S. G. Deo: Differential Systems Involving Impulses. Lecture Notes in Mathematics 954. Springer, Berlin (1982). DOI 10.1007/BFb0067476 | MR 0674119 | Zbl 0539.34001
[33] J. Persson: Regularization of nonlinear measure differential equations. Matematiche 44 (1989), 113-130. MR 1093156 | Zbl 0715.34005
[34] S. Saks: Theory of the Integral. Dover, New York (1964). MR 0167578 | Zbl 1196.28001
[35] A. M. Samoilenko, N. A. Perestyuk: Impulsive Differential Equations. World Scientific Series on Nonlinear Science. Series A. 14. World Scientific, Singapore (1995). DOI 10.1142/2892 | MR 1355787 | Zbl 0837.34003
[36] W. W. Schmaedeke: Optimal control theory for nonlinear vector differential equations containing measures. J. Soc. Ind. Appl. Math., Ser. A, Control 3 (1965), 231-280. DOI 10.1137/0303019 | MR 0189870 | Zbl 0161.29203
[37] Š. Schwabik, M. Tvrdý, O. Vejvoda: Differential and Integral Equations: Boundary Value Problems and Adjoints. Academia, Praha (1979). MR 0542283 | Zbl 0417.45001
[38] A. Slavík: Well-posedness results for abstract generalized differential equations and measure functional differential equations. J. Differ. Equations 259 (2015), 666-707. DOI 10.1016/j.jde.2015.02.013 | MR 3338315 | Zbl 1319.34116
[39] V. E. Slyusarchuk: General theorems on the existence and uniqueness of solutions to impulsive differential equations. Ukr. Math. J. 52 (2000), 1094-1106. DOI 10.1023/A:1005281717641 | MR 1817324 | Zbl 0976.34010
[40] G. T. Stamov: Almost Periodic Solutions of Impulsive Differential Equations. Lecture Notes in Mathematics 2047. Springer, Berlin (2012). DOI 10.1007/978-3-642-27546-3 | MR 2934087 | Zbl 1255.34001
[41] I. Stamova, G. Stamov: Applied Impulsive Mathematical Models. CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC. Springer, Cham (2016). DOI 10.1007/978-3-319-28061-5 | MR 3496133 | Zbl 1355.34004
[42] A. Tanwani, B. Brogliato, C. Prieur: Stability notions for a class of nonlinear systems with measure controls. Math. Control Signals Syst. 27 (2015), 245-275. DOI 10.1007/s00498-015-0140-7 | MR 3343941 | Zbl 1327.93330
[43] N. van de Wouw, R. I. Leine: Tracking control for a class of measure differential inclusions. 47th IEEE Conference on Decision and Control IEEE, Philadelphia (2008), 2526-2532. DOI 10.1109/CDC.2008.4738683
[44] A. Yablonski: Differential equations with generalized coefficients. Nonlinear Anal., Theory Methods Appl., Ser. A 63 (2005), 171-197. DOI 10.1016/j.na.2005.03.108 | MR 2165495 | Zbl 1089.34006
[45] S. T. Zavalishchin, A. N. Sesekin: Dynamic Impulse Systems: Theory and Applications. Mathematics and its Applications (Dordrecht) 394. Kluwer, Dordrecht (1997). DOI 10.1007/978-94-015-8893-5 | MR 1441079 | Zbl 0880.46031
[46] W. P. Ziemer: Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation. Graduate Texts in Mathematics 120. Springer, Berlin (1989). DOI 10.1007/978-1-4612-1015-3 | MR 1014685 | Zbl 0692.46022