• Previous Article
    Radially symmetric solutions of an anisotropic mean curvature equation modeling the corneal shape
  • PROC Home
  • This Issue
  • Next Article
    Existence of nontrivial solutions for equations of $p(x)$-Laplace type without Ambrosetti and Rabinowitz condition
2015, 2015(special): 287-296. doi: 10.3934/proc.2015.0287

On the properties of solutions set for measure driven differential inclusions

1. 

Faculty of Mathematics and Computer Science, A. Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

2. 

Faculty of Electrical Engineering and Computer Science, Stefan cel Mare University, Universitatii 13, 720229 Suceava, Romania

Received  July 2014 Revised  November 2014 Published  November 2015

The aim of the paper is to present properties of solutions set for differential inclusions driven by a positive finite Borel measure. We provide for the most natural type of solution results concerning the continuity of the solution set with respect to the data similar to some already known results, available for different types of solutions. As consequence, the solution set is shown to be compact as a subset of the space of regulated functions. The results allow one (by taking the measure $\mu$ of a particular form) to obtain information on the solution set for continuous or discrete problems, as well as impulsive or retarded set-valued problems.
Citation: Mieczysław Cichoń, Bianca Satco. On the properties of solutions set for measure driven differential inclusions. Conference Publications, 2015, 2015 (special) : 287-296. doi: 10.3934/proc.2015.0287
References:
[1]

Birkhäuser, Boston, 1990.  Google Scholar

[2]

in "DCBMS-NSF Regional Conference Series in Applied Mathematics", 1971.  Google Scholar

[3]

Prentice-Hall, 1997. Google Scholar

[4]

in Lecture Notes in Math. 580, Springer, Berlin, 1977.  Google Scholar

[5]

Adv. Diff. Equations 2014, 2014:56, 18 pp. Google Scholar

[6]

Differential Integral Equations 4 (1991), 739-765.  Google Scholar

[7]

J. Diff. Equations 252 (2012), 3816-3847.  Google Scholar

[8]

Math. Bohem. 116 (1991), 20-59.  Google Scholar

[9]

Torres Fremlin, Colchester (2003).  Google Scholar

[10]

Funct. Differ. Equ. 16 (2009), 299-313.  Google Scholar

[11]

Jour. Multivariate Anal. 51 (1994), 252-264.  Google Scholar

[12]

in "Hybrid Systems: Computation and Control", Lecture Notes in Computer Science 4416 (2007), 385-398.  Google Scholar

[13]

J. Math. Syst. Estimation and Control 4 (1994), 1-21.  Google Scholar

[14]

Kluwer Academic Publishers, Dordrecht, 2003.  Google Scholar

[15]

Discrete Contin. Dyn. Syst. 33 (2013), 283-303.  Google Scholar

[16]

Bull. Belg. Math. Soc. 2 (1995), 381-388.  Google Scholar

[17]

The Annals of Mathematical Statistics 33 (1962), 659-680.  Google Scholar

[18]

Monografie Matematyczne, Warszawa, 1937. Google Scholar

[19]

Dordrecht, Praha, 1979.  Google Scholar

[20]

Dordrecht, Kluwer Academic, 1997.  Google Scholar

[21]

J. Math. Anal. Appl. 202 (1996), 727-746.  Google Scholar

[22]

Journal of Differential Equations 259 (2015), 666-707. Google Scholar

[23]

Habil. Thesis, Praha, 2001. Google Scholar

show all references

References:
[1]

Birkhäuser, Boston, 1990.  Google Scholar

[2]

in "DCBMS-NSF Regional Conference Series in Applied Mathematics", 1971.  Google Scholar

[3]

Prentice-Hall, 1997. Google Scholar

[4]

in Lecture Notes in Math. 580, Springer, Berlin, 1977.  Google Scholar

[5]

Adv. Diff. Equations 2014, 2014:56, 18 pp. Google Scholar

[6]

Differential Integral Equations 4 (1991), 739-765.  Google Scholar

[7]

J. Diff. Equations 252 (2012), 3816-3847.  Google Scholar

[8]

Math. Bohem. 116 (1991), 20-59.  Google Scholar

[9]

Torres Fremlin, Colchester (2003).  Google Scholar

[10]

Funct. Differ. Equ. 16 (2009), 299-313.  Google Scholar

[11]

Jour. Multivariate Anal. 51 (1994), 252-264.  Google Scholar

[12]

in "Hybrid Systems: Computation and Control", Lecture Notes in Computer Science 4416 (2007), 385-398.  Google Scholar

[13]

J. Math. Syst. Estimation and Control 4 (1994), 1-21.  Google Scholar

[14]

Kluwer Academic Publishers, Dordrecht, 2003.  Google Scholar

[15]

Discrete Contin. Dyn. Syst. 33 (2013), 283-303.  Google Scholar

[16]

Bull. Belg. Math. Soc. 2 (1995), 381-388.  Google Scholar

[17]

The Annals of Mathematical Statistics 33 (1962), 659-680.  Google Scholar

[18]

Monografie Matematyczne, Warszawa, 1937. Google Scholar

[19]

Dordrecht, Praha, 1979.  Google Scholar

[20]

Dordrecht, Kluwer Academic, 1997.  Google Scholar

[21]

J. Math. Anal. Appl. 202 (1996), 727-746.  Google Scholar

[22]

Journal of Differential Equations 259 (2015), 666-707. Google Scholar

[23]

Habil. Thesis, Praha, 2001. Google Scholar

[1]

Saima Rashid, Fahd Jarad, Zakia Hammouch. Some new bounds analogous to generalized proportional fractional integral operator with respect to another function. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021020

[2]

Zengyun Wang, Jinde Cao, Zuowei Cai, Lihong Huang. Finite-time stability of impulsive differential inclusion: Applications to discontinuous impulsive neural networks. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2677-2692. doi: 10.3934/dcdsb.2020200

[3]

Changpin Li, Zhiqiang Li. Asymptotic behaviors of solution to partial differential equation with Caputo–Hadamard derivative and fractional Laplacian: Hyperbolic case. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021023

[4]

Zhiming Guo, Zhi-Chun Yang, Xingfu Zou. Existence and uniqueness of positive solution to a non-local differential equation with homogeneous Dirichlet boundary condition---A non-monotone case. Communications on Pure & Applied Analysis, 2012, 11 (5) : 1825-1838. doi: 10.3934/cpaa.2012.11.1825

[5]

Wei Liu, Pavel Krejčí, Guoju Ye. Continuity properties of Prandtl-Ishlinskii operators in the space of regulated functions. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3783-3795. doi: 10.3934/dcdsb.2017190

[6]

Charlene Kalle, Niels Langeveld, Marta Maggioni, Sara Munday. Matching for a family of infinite measure continued fraction transformations. Discrete & Continuous Dynamical Systems, 2020, 40 (11) : 6309-6330. doi: 10.3934/dcds.2020281

[7]

Ugo Bessi. Another point of view on Kusuoka's measure. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3241-3271. doi: 10.3934/dcds.2020404

[8]

Andreia Chapouto. A remark on the well-posedness of the modified KdV equation in the Fourier-Lebesgue spaces. Discrete & Continuous Dynamical Systems, 2021, 41 (8) : 3915-3950. doi: 10.3934/dcds.2021022

[9]

Julian Tugaut. Captivity of the solution to the granular media equation. Kinetic & Related Models, 2021, 14 (2) : 199-209. doi: 10.3934/krm.2021002

[10]

Sara Munday. On the derivative of the $\alpha$-Farey-Minkowski function. Discrete & Continuous Dynamical Systems, 2014, 34 (2) : 709-732. doi: 10.3934/dcds.2014.34.709

[11]

Chaoqian Li, Yajun Liu, Yaotang Li. Note on $ Z $-eigenvalue inclusion theorems for tensors. Journal of Industrial & Management Optimization, 2021, 17 (2) : 687-693. doi: 10.3934/jimo.2019129

[12]

Xue-Ping Luo, Yi-Bin Xiao, Wei Li. Strict feasibility of variational inclusion problems in reflexive Banach spaces. Journal of Industrial & Management Optimization, 2020, 16 (5) : 2495-2502. doi: 10.3934/jimo.2019065

[13]

Mansour Shrahili, Ravi Shanker Dubey, Ahmed Shafay. Inclusion of fading memory to Banister model of changes in physical condition. Discrete & Continuous Dynamical Systems - S, 2020, 13 (3) : 881-888. doi: 10.3934/dcdss.2020051

[14]

Ruchika Sehgal, Aparna Mehra. Worst-case analysis of Gini mean difference safety measure. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1613-1637. doi: 10.3934/jimo.2020037

[15]

Guido De Philippis, Antonio De Rosa, Jonas Hirsch. The area blow up set for bounded mean curvature submanifolds with respect to elliptic surface energy functionals. Discrete & Continuous Dynamical Systems, 2019, 39 (12) : 7031-7056. doi: 10.3934/dcds.2019243

[16]

Wenbin Li, Jianliang Qian. Simultaneously recovering both domain and varying density in inverse gravimetry by efficient level-set methods. Inverse Problems & Imaging, 2021, 15 (3) : 387-413. doi: 10.3934/ipi.2020073

[17]

Joel Fotso Tachago, Giuliano Gargiulo, Hubert Nnang, Elvira Zappale. Multiscale homogenization of integral convex functionals in Orlicz Sobolev setting. Evolution Equations & Control Theory, 2021, 10 (2) : 297-320. doi: 10.3934/eect.2020067

[18]

Oleksandr Boichuk, Victor Feruk. Boundary-value problems for weakly singular integral equations. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021094

[19]

Anderson L. A. de Araujo, Marcelo Montenegro. Existence of solution and asymptotic behavior for a class of parabolic equations. Communications on Pure & Applied Analysis, 2021, 20 (3) : 1213-1227. doi: 10.3934/cpaa.2021017

[20]

Yumi Yahagi. Construction of unique mild solution and continuity of solution for the small initial data to 1-D Keller-Segel system. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021099

 Impact Factor: 

Metrics

  • PDF downloads (82)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]