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Volumn 219, Issue 1, 2012, Pages 289-305

On set differential equations in Banach spaces - A second type Hukuhara differentiability approach

Author keywords

Comparison principle; Existence and uniqueness theorem; Global solution; Local solution; Second type Hukuhara derivative; Set differential equation in Banach space

Indexed keywords

CAUCHY PROBLEMS; COMPARISON PRINCIPLE; COMPARISON RESULT; DIFFERENTIABILITY; EXISTENCE AND UNIQUENESS THEOREM; GLOBAL SOLUTIONS; SET DIFFERENTIAL EQUATIONS; SUCCESSIVE APPROXIMATIONS;

EID: 84864286918     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2012.06.019     Document Type: Conference Paper
Times cited : (44)

References (44)
  • 1
    • 33749047628 scopus 로고    scopus 로고
    • Dynamics and stability of impulsive hybrid setvalued integro-differential equations with delay
    • B. Ahmad, and S. Sivasundaram Dynamics and stability of impulsive hybrid setvalued integro-differential equations with delay Nonlinear Anal. TMA 65 2006 2082 2093
    • (2006) Nonlinear Anal. TMA , vol.65 , pp. 2082-2093
    • Ahmad, B.1    Sivasundaram, S.2
  • 2
    • 33750060080 scopus 로고    scopus 로고
    • The monotone iterative technique for impulsive hybrid set valued integro-differential equations
    • B. Ahmad, and S. Sivasundaram The monotone iterative technique for impulsive hybrid set valued integro-differential equations Nonlinear Anal. TMA 65 2006 2260 2276
    • (2006) Nonlinear Anal. TMA , vol.65 , pp. 2260-2276
    • Ahmad, B.1    Sivasundaram, S.2
  • 3
    • 34547499060 scopus 로고    scopus 로고
    • Setvalued perturbed hybrid integro-differential equations and stability in term of two measures
    • B. Ahmad, and S. Sivasundaram Setvalued perturbed hybrid integro-differential equations and stability in term of two measures Dynam. Syst. Appl. 16 2007 299 310
    • (2007) Dynam. Syst. Appl. , vol.16 , pp. 299-310
    • Ahmad, B.1    Sivasundaram, S.2
  • 4
    • 49249090910 scopus 로고    scopus 로고
    • Stability in term of two measures for setvalued perturbed impulsive delay differential equations
    • B. Ahmad, and S. Sivasundaram Stability in term of two measures for setvalued perturbed impulsive delay differential equations Commun. Appl. Anal. 12 2008 57 68
    • (2008) Commun. Appl. Anal. , vol.12 , pp. 57-68
    • Ahmad, B.1    Sivasundaram, S.2
  • 5
    • 69549086687 scopus 로고    scopus 로고
    • φ 0-stability of impulsive hybrid setvalued differential equations with delay by perturbing Lyapunov functions
    • φ 0-stability of impulsive hybrid setvalued differential equations with delay by perturbing Lyapunov functions Commun. Appl. Anal. 12 2008 137 146
    • (2008) Commun. Appl. Anal. , vol.12 , pp. 137-146
    • Ahmad, B.1    Sivasundaram, S.2
  • 7
    • 50549204934 scopus 로고
    • Integrals of set-valued functions
    • R.J. Aumann Integrals of set-valued functions J. Math. Anal. Appl. 12 1965 1 12
    • (1965) J. Math. Anal. Appl. , vol.12 , pp. 1-12
    • Aumann, R.J.1
  • 8
    • 0014742116 scopus 로고
    • A differential calculus for multifunctions
    • H.T. Banks, and M.Q. Jacobs A differential calculus for multifunctions J. Math. Anal. Appl. 29 1970 246 272
    • (1970) J. Math. Anal. Appl. , vol.29 , pp. 246-272
    • Banks, H.T.1    Jacobs, M.Q.2
  • 9
    • 70349784604 scopus 로고    scopus 로고
    • Topological structure of solution sets to differential problems in Fréchet spaces
    • A. Ba̧kowska, and G. Gabor Topological structure of solution sets to differential problems in Fréchet spaces Ann. Polon. Math. 95 2009 17 35
    • (2009) Ann. Polon. Math. , vol.95 , pp. 17-35
    • Ba̧kowska, A.1    Gabor, G.2
  • 10
    • 12844285437 scopus 로고
    • Equazioni differenziali con soluzioni a valore compatto convesso
    • F.S. de Blasi, and F. Iervolino Equazioni differenziali con soluzioni a valore compatto convesso Boll. Unione Mat. Ital. 4 1969 491 501
    • (1969) Boll. Unione Mat. Ital. , vol.4 , pp. 491-501
    • De Blasi, F.S.1    Iervolino, F.2
  • 11
    • 34248596883 scopus 로고
    • Uniqueness and existence theorems for differential equations with convex valued solutions
    • A.I. Brandão Lopes Pinto, F.S. de Blasi, and F. Iervolino Uniqueness and existence theorems for differential equations with convex valued solutions Boll. Unione Mat. Ital. 4 1970 1 12
    • (1970) Boll. Unione Mat. Ital. , vol.4 , pp. 1-12
    • Brandão Lopes Pinto, A.I.1    De Blasi, F.S.2    Iervolino, F.3
  • 13
    • 60349110519 scopus 로고    scopus 로고
    • Stability results for set differential equations with causal maps
    • Z. Drici, F.A. McRae, and J. Vasundhara Devi Stability results for set differential equations with causal maps Dynam. Syst. Appl. 15 2006 451 463
    • (2006) Dynam. Syst. Appl. , vol.15 , pp. 451-463
    • Drici, Z.1    McRae, F.A.2    Vasundhara Devi, J.3
  • 14
    • 14644437111 scopus 로고    scopus 로고
    • Set valued functions in Fréchet spaces: Continuity, Hukuhara differentiability and applications to set differential equations
    • G.N. Galanis, T. Gnana Bhaskar, V. Lakshmikantham, and P.K. Palamides Set valued functions in Fréchet spaces: Continuity, Hukuhara differentiability and applications to set differential equations Nonlinear Anal. TMA 61 2005 559 575
    • (2005) Nonlinear Anal. TMA , vol.61 , pp. 559-575
    • Galanis, G.N.1    Gnana Bhaskar, T.2    Lakshmikantham, V.3    Palamides, P.K.4
  • 15
    • 0042412264 scopus 로고    scopus 로고
    • Set differential equations and flow invariance
    • T. Gnana Bhaskar, and V. Lakshmikantham Set differential equations and flow invariance Appl. Anal. 82 2003 357 368
    • (2003) Appl. Anal. , vol.82 , pp. 357-368
    • Gnana Bhaskar, T.1    Lakshmikantham, V.2
  • 16
    • 28044468648 scopus 로고    scopus 로고
    • Nonlinear variation of parameters formula for set differential equations in a metric space
    • T. Gnana Bhaskar, V. Lakshmikantham, and J. Vasundhara Devi Nonlinear variation of parameters formula for set differential equations in a metric space Nonlinear Anal. TMA 63 2005 735 744
    • (2005) Nonlinear Anal. TMA , vol.63 , pp. 735-744
    • Gnana Bhaskar, T.1    Lakshmikantham, V.2    Vasundhara Devi, J.3
  • 20
    • 0012777173 scopus 로고
    • Intégration des applications mesurables dont la valeur est un compact convexe
    • M. Hukuhara Intégration des applications mesurables dont la valeur est un compact convexe Funkcial. Ekvac. 10 1967 205 223
    • (1967) Funkcial. Ekvac. , vol.10 , pp. 205-223
    • Hukuhara, M.1
  • 22
    • 12744250114 scopus 로고
    • Method of averaging for differential equations with compact convex valued solutions
    • M. Kisielewicz Method of averaging for differential equations with compact convex valued solutions Rend. Mat. 9 1976 397 408
    • (1976) Rend. Mat. , vol.9 , pp. 397-408
    • Kisielewicz, M.1
  • 24
    • 34248587149 scopus 로고
    • Existence theorem for functional differential equations with compact convex valued solutions
    • M. Kisielewicz, B. Serafin, and W. Sosulski Existence theorem for functional differential equations with compact convex valued solutions Demonstr. Math. 9 1976 229 237
    • (1976) Demonstr. Math. , vol.9 , pp. 229-237
    • Kisielewicz, M.1    Serafin, B.2    Sosulski, W.3
  • 26
    • 15544370865 scopus 로고    scopus 로고
    • Set differential equations versus fuzzy differential equations
    • V. Lakshmikantham Set differential equations versus fuzzy differential equations Appl. Math. Comput. 164 2005 277 294
    • (2005) Appl. Math. Comput. , vol.164 , pp. 277-294
    • Lakshmikantham, V.1
  • 30
    • 0038137267 scopus 로고    scopus 로고
    • Interconnection between set and fuzzy differential equations
    • V. Lakshmikantham, S. Leela, and A.S. Vatsala Interconnection between set and fuzzy differential equations Nonlinear Anal. TMA 54 2003 351 360
    • (2003) Nonlinear Anal. TMA , vol.54 , pp. 351-360
    • Lakshmikantham, V.1    Leela, S.2    Vatsala, A.S.3
  • 32
    • 0041387380 scopus 로고    scopus 로고
    • Existence and interrelation between set and fuzzy differential equations
    • V. Lakshmikantham, and A.A. Tolstonogov Existence and interrelation between set and fuzzy differential equations Nonlinear Anal. TMA 55 2003 255 268
    • (2003) Nonlinear Anal. TMA , vol.55 , pp. 255-268
    • Lakshmikantham, V.1    Tolstonogov, A.A.2
  • 33
    • 79961173984 scopus 로고    scopus 로고
    • Interval differential equations with a second type Hukuhara derivative
    • M.T. Malinowski Interval differential equations with a second type Hukuhara derivative Appl. Math. Lett. 24 2011 2118 2123
    • (2011) Appl. Math. Lett. , vol.24 , pp. 2118-2123
    • Malinowski, M.T.1
  • 34
    • 84860460941 scopus 로고    scopus 로고
    • Second type Hukuhara differentiable solutions to the delay set-valued differential equations
    • M.T. Malinowski Second type Hukuhara differentiable solutions to the delay set-valued differential equations Appl. Math. Comput. 218 2012 9427 9437
    • (2012) Appl. Math. Comput. , vol.218 , pp. 9427-9437
    • Malinowski, M.T.1
  • 35
    • 84863715655 scopus 로고    scopus 로고
    • Interval Cauchy problem with a second type Hukuhara derivative
    • 10.1016/j.ins.2012.05.022
    • M.T. Malinowski Interval Cauchy problem with a second type Hukuhara derivative Inform. Sci. 2012 10.1016/j.ins.2012.05.022
    • (2012) Inform. Sci.
    • Malinowski, M.T.1
  • 36
    • 33749061013 scopus 로고    scopus 로고
    • Impulsive set differential equations with delay
    • F.A. McRae, and J. Vasundhara Devi Impulsive set differential equations with delay Applicable Anal. 84 2005 329 341
    • (2005) Applicable Anal. , vol.84 , pp. 329-341
    • McRae, F.A.1    Vasundhara Devi, J.2
  • 37
    • 53949118548 scopus 로고    scopus 로고
    • Stability criteria for set control differential equations
    • N.D. Phu, L.T. Quang, and T.T. Tung Stability criteria for set control differential equations Nonlinear Anal. TMA 69 2008 3715 3721
    • (2008) Nonlinear Anal. TMA , vol.69 , pp. 3715-3721
    • Phu, N.D.1    Quang, L.T.2    Tung, T.T.3
  • 38
    • 25144468599 scopus 로고    scopus 로고
    • Averaging in differential equations with Hukuhara derivative and delay
    • A.V. Plotnikov, and P.I. Rashkov Averaging in differential equations with Hukuhara derivative and delay Funct. Diff. Equ. 8 2001 371 381
    • (2001) Funct. Diff. Equ. , vol.8 , pp. 371-381
    • Plotnikov, A.V.1    Rashkov, P.I.2
  • 39
    • 84968480766 scopus 로고
    • An embedding theorem for spaces of convex sets
    • H. Radström An embedding theorem for spaces of convex sets Proc. Am. Math. Soc. 3 1952 165 169
    • (1952) Proc. Am. Math. Soc. , vol.3 , pp. 165-169
    • Radström, H.1
  • 40
    • 67349163185 scopus 로고    scopus 로고
    • Generalized Hukuhara differentiability of interval-valued functions and interval differential equations
    • L. Stefanini, and B. Bede Generalized Hukuhara differentiability of interval-valued functions and interval differential equations Nonlinear Anal. TMA 71 2009 1311 1328
    • (2009) Nonlinear Anal. TMA , vol.71 , pp. 1311-1328
    • Stefanini, L.1    Bede, B.2
  • 42
    • 67349278129 scopus 로고    scopus 로고
    • Stability of set differential equations and applications
    • N.N. Tu, and T.T. Tung Stability of set differential equations and applications Nonlinear Anal. TMA 71 2009 1526 1533
    • (2009) Nonlinear Anal. TMA , vol.71 , pp. 1526-1533
    • Tu, N.N.1    Tung, T.T.2
  • 43
    • 79957816618 scopus 로고    scopus 로고
    • Existence, uniqueness of solutions for set differential equations involving causal operators with memory
    • J. Vasundhara Devi Existence, uniqueness of solutions for set differential equations involving causal operators with memory Eur. J. Pure Appl. Math. 3 2010 737 747
    • (2010) Eur. J. Pure Appl. Math. , vol.3 , pp. 737-747
    • Vasundhara Devi, J.1


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