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Title: Equations containing locally Henstock-Kurzweil integrable functions (English)
Author: Heikkilä, Seppo
Author: Ye, Guoju
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 57
Issue: 6
Year: 2012
Pages: 569-580
Summary lang: English
Category: math
Summary: A fixed point theorem in ordered spaces and a recently proved monotone convergence theorem are applied to derive existence and comparison results for solutions of a functional integral equation of Volterra type and a functional impulsive Cauchy problem in an ordered Banach space. A novel feature is that equations contain locally Henstock-Kurzweil integrable functions. (English)
Keyword: integrability
Keyword: Henstock-Kurzweil integral
Keyword: ordered Banach space
Keyword: order cone
Keyword: chain
Keyword: fixed point
Keyword: functional integral equation
Keyword: Volterra
Keyword: Cauchy problem
Keyword: ordered Banach space
Keyword: fixed point
MSC: 26A39
MSC: 28B15
MSC: 34A36
MSC: 34A37
MSC: 45N05
MSC: 46B40
MSC: 47H07
MSC: 47H10
idZBL: Zbl 1274.45017
idMR: MR3010237
DOI: 10.1007/s10492-012-0034-7
Date available: 2012-11-10T20:38:48Z
Last updated: 2020-07-02
Stable URL:
Reference: [1] Carl, S., Heikkilä, S.: On discontinuous implicit and explicit abstract impulsive boundary value problems.Nonlinear Anal., Theory Methods Appl. 41 (2000), 701-723. MR 1780640, 10.1016/S0362-546X(98)00305-8
Reference: [2] Federson, M., Bianconi, M.: Linear Fredholm integral equations and the integral of Kurzweil.J. Appl. Anal. 8 (2002), 83-110. Zbl 1043.45010, MR 1921473, 10.1515/JAA.2002.83
Reference: [3] Federson, M., Schwabik, Š.: Generalized ordinary differential equations approach to impulsive retarded functional differential equations.Differ. Integral Equ. 19 (2006), 1201-1234. MR 2278005
Reference: [4] Federson, M., Táboas, P.: Impulsive retarded differential equations in Banach spaces via Bochner-Lebesgue and Henstock integrals.Nonlinear Anal., Theory Methods Appl. 50 (2002), 389-407. Zbl 1011.34070, MR 1906469, 10.1016/S0362-546X(01)00769-6
Reference: [5] Guo, D., Cho, Y. J., Zhu, J.: Partial Ordering Methods in Nonlinear Problems.Nova Science Publishers, Inc. New York (2004). Zbl 1116.45007, MR 2084490
Reference: [6] Heikkilä, S., Kumpulainen, S., Kumpulainen, M.: On improper integrals and differential equations in ordered Banach spaces.J. Math. Anal. Appl. 319 (2006), 579-603. Zbl 1105.34037, MR 2227925, 10.1016/j.jmaa.2005.06.051
Reference: [7] Heikkilä, S., Lakshmikantham, V.: Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations.Marcel Dekker, Inc. New York (1994). Zbl 0804.34001, MR 1280028
Reference: [8] Heikkilä, S., Seikkala, S.: On non-absolute functional Volterra integral equations and impulsive differential equations in ordered Banach spaces.Electron. J. Differ. Equ., paper No. 103 (2008), 1-11. Zbl 1168.45011, MR 2430900
Reference: [9] Heikkilä, S., Ye, G.: Convergence and comparison results for Henstock-Kurzweil and McShane integrable vector-valued functions.Southeast Asian Bull. Math. 35 (2011), 407-418. Zbl 1240.26025, MR 2856387
Reference: [10] Lu, J., Lee, P.-Y.: On singularity of Henstock integrable functions.Real Anal. Exch. 25 (2000), 795-797. Zbl 1015.26016, MR 1778532, 10.2307/44154035
Reference: [11] Satco, B.-R.: Nonlinear Volterra integral equations in Henstock integrability setting.Electron. J. Differ. Equ., paper No. 39 (2008), 1-9. Zbl 1169.45300, MR 2392943
Reference: [12] Schwabik, Š., Ye, G.: Topics in Banach Space Integration.World Scientific Hackensack (2005). Zbl 1088.28008, MR 2167754
Reference: [13] Sikorska-Nowak, A.: On the existence of solutions of nonlinear integral equations in Banach spaces and Henstock-Kurzweil integrals.Ann. Pol. Math. 83 (2004), 257-267. Zbl 1101.45006, MR 2111712, 10.4064/ap83-3-7
Reference: [14] Sikorska-Nowak, A.: Existence theory for integrodifferential equations and Henstock-Kurzweil integral on Banach spaces.J. Appl. Math., Article ID31572 (2007), 1-12. MR 2317885, 10.1155/2007/31572
Reference: [15] Sikorska-Nowak, A.: Existence of solutions of nonlinear integral equations in Banach spaces and Henstock-Kurzweil integrals.Ann. Soc. Math. Pol., Ser. I, Commentat. Math. 47 (2007), 227-238. MR 2377959
Reference: [16] Sikorska-Nowak, A.: Nonlinear integrodifferential equations of mixed type in Banach spaces.Int. J. Math. Math. Sci., Article ID65947 (2007), 1-14. Zbl 1147.45009, MR 2336140, 10.1155/2007/65947
Reference: [17] Sikorska-Nowak, A.: Nonlinear integral equations in Banach spaces and Henstock-Kurzweil-Pettis integrals.Dyn. Syst. Appl. 17 (2008), 97-107. Zbl 1154.45011, MR 2433893


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