[1] Agarwal R., O'Regan D., Sikorska-Nowak A.:
The set of solutions of integrodifferential equations and the Henstock-Kurzweil-Pettis integral in Banach spaces. Bull. Austral. Math. Soc. 78 (2008), 507–522.
DOI 10.1017/S0004972708000944 |
MR 2472285
[2] Aliprantis C.D., Border K.C.:
Infinite Dimensional Analysis. third edition, Springer, Berlin, 2006.
MR 2378491 |
Zbl 1156.46001
[3] Ben Amar A., Mnif M.:
Leray-Schauder alternatives for weakly sequentially continuous mappings and application to transport equation. Math. Methods Appl. Sci. 33 (2010), no. 1, 80–90.
MR 2591226 |
Zbl 1193.47056
[4] Bugajewski D.:
On the existence of weak solutions of integral equations in Banach spaces. Comment. Math. Univ. Carolin. 35 (1994), no. 1, 35–41.
MR 1292580 |
Zbl 0816.45012
[5] Chew T.S., Flordeliza F.:
On $x'=f(t,x)$ and Henstock-Kurzweil integrals. Differential Integral Equations 4 (1991), 861–868.
MR 1108065 |
Zbl 0733.34004
[7] Cichoń M.:
Weak solutions of differential equations in Banach spaces. Discuss. Math. Differential Incl. 15 (1995), 5–14.
MR 1344523
[8] Cichoń M., Kubiaczyk I.:
On the set of solutions of the Cauchy problem in Banach spaces. Arch. Math. (Basel) 63 (1994), 251–257.
DOI 10.1007/BF01189827 |
MR 1287254
[9] Cramer E., Lakshmikantham V., Mitchell A.R.:
On the existence of weak solution of differential equations in nonreflexive Banach spaces. Nonlinear Anal. 2 (1978), 169–177.
MR 0512280
[10] DeBlasi F.S.:
On a property of the unit sphere in Banach space. Bull. Math. Soc. Sci. Math. R.S. Roumanie (NS) 21 (1977), 259–262.
MR 0482402
[11] Diestel J., Uhl J.J.:
Vector Measures. Mathematical Surveys, 15, American Mathematical Society, Providence, R.I., 1977.
MR 0453964 |
Zbl 0521.46035
[12] Di Piazza L.:
Kurzweil-Henstock type integration on Banach spaces. Real Anal. Exchange 29 (2003/04), no. 2, 543–555.
MR 2083796 |
Zbl 1083.28007
[14] Federson M., Bianconi R.:
Linear integral equations of Volterra concerning Henstock integrals. Real Anal. Exchange 25 (1999/00), 389–417.
MR 1758896 |
Zbl 1015.45001
[15] Federson M., Táboas P.:
Impulsive retarded differential equations in Banach spaces via Bochner-Lebesgue and Henstock integrals. Nonlinear Anal. 50 (1998), 389–407.
DOI 10.1016/S0362-546X(01)00769-6 |
MR 1906469
[16] Gamez J.L., Mendoza J.:
On Denjoy-Dunford and Denjoy-Pettis integrals. Studia Math. 130 (1998), 115–133.
MR 1623348 |
Zbl 0971.28009
[18] Gordon R.A.:
The Integrals of Lebesgue, Denjoy, Perron and Henstock. Graduate Studies in Mathematics, 4, American Mathematical Society, Providence, RI, 1994.
MR 1288751 |
Zbl 0807.26004
[20] Kubiaczyk I., Szufla S.:
Kenser's theorem for weak solutions of ordinary differential equations in Banach spaces. Publ. Inst. Math. (Beograd) (N.S.) 32(46) (1982), 99–103.
MR 0710975
[21] Kubiaczyk I.:
On the existence of solutions of differential equations in Banach spaces. Bull. Polish Acad. Sci. Math. 33 (1985), 607–614.
MR 0849409 |
Zbl 0607.34055
[22] Kurtz D.S., Swartz C.W.:
Theories of Integration: The Integrals of Riemann, Lebesgue, Henstock-Kurzweil, and Mcshane. World Scientific, Singapore, 2004.
MR 2081182 |
Zbl 1072.26005
[23] Martin R.H.:
Nonlinear Operators and Differential Equations in Banach Spaces. Wiley-Interscience, New York-London-Sydney, 1976.
MR 0492671 |
Zbl 0333.47023
[24] Mitchell A.R., Smith C.:
An existence theorem for weak solutions of differential equations in Banach spaces. in Nonlinear Equations in Abstract Spaces (Proc. Internat. Sympos., Univ. Texas, Arlington, Tex, 1977), pp. 387–403, Academic Press, New York, 1978.
MR 0502554 |
Zbl 0452.34054
[25] Lakshmikantham V., Leela S.:
Nonlinear Differential Equations in Abstract Spaces. Pergamon Press, Oxford-New York, 1981.
MR 0616449 |
Zbl 0456.34002
[26] Lee P.Y.:
Lanzhou Lectures on Henstock Integration. Series in Real Analysis, 2, World Scientific, Teaneck, NJ, 1989.
MR 1050957 |
Zbl 0699.26004
[30] Satco B.:
A Komlós-type theorem for the set-valued Henstock-Kurzweil-Pettis integrals and applications. Czechoslovak Math. J. 56(131) (2006), 1029–1047.
DOI 10.1007/s10587-006-0078-5 |
MR 2261675
[33] Schwabik S.:
The Perron integral in ordinary differential equations. Differential Integral Equations 6 (1993), 863–882.
MR 1222306 |
Zbl 0784.34006
[34] Schwabik S., Guoju Y.:
Topics in Banach Space Integration. World Scientific, Hackensack, NJ, 2005.
MR 2167754 |
Zbl 1088.28008
[35] Sikorska A.:
Existence theory for nonlinear Volterra integral and differential equations. J. Inequal. Appl. 6 (3) (2001), 325–338.
MR 1889019 |
Zbl 0992.45006
[36] Sikorska-Nowak A.:
Retarded functional differential equations in Banach spaces and Henstock-Kurzweil integrals. Demonstratio Math. 35 (2002), no. 1, 49–60.
MR 1883943 |
Zbl 1011.34066
[37] Sikorska-Nowak A.:
On the existence of solutions of nonlinear integral equations in Banach spaces and Henstock-Kurzweil integrals. Ann. Polon. Math. 83 (2004), no. 3,257–267.
DOI 10.4064/ap83-3-7 |
MR 2111712 |
Zbl 1101.45006
[38] Sikorska-Nowak A.:
The existence theory for the differential equation $x^{(m)}t=f(t,x)$ in Banach spaces and Henstock-Kurzweil integral. Demonstratio Math. 40 (2007), no. 1, 115–124.
MR 2330370 |
Zbl 1128.34037
[39] Sikorska-Nowak A.:
Retarded functional differential equations in Banach spaces and Henstock-Kurzweil-Pettis integrals. Discuss. Math. Differ. Incl. Control Optim. 27 (2007), 315–327.
DOI 10.7151/dmdico.1087 |
MR 2413816 |
Zbl 1149.34053
[40] Sikorska-Nowak A.:
Existence of solutions of nonlinear integral equations and Henstock-Kurzweil integrals. Comment. Math. Prace Mat. 47 (2007), no. 2, 227–238.
MR 2377959 |
Zbl 1178.45016
[41] Sikorska-Nowak A.:
Existence theory for integrodifferential equations and Henstock-Kurzweil integral in Banach spaces. J. Appl. Math. 2007, article ID 31572, 12 pp.
MR 2317885 |
Zbl 1148.26010
[42] Sikorska-Nowak A.:
Nonlinear integral equations in Banach spaces and Henstock-Kurzweil-Pettis integrals. Dynam. Systems Appl. 17 (2008), 97–107.
MR 2433893 |
Zbl 1154.45011
[43] Szufla S.:
Kneser's theorem for weak solutions of ordinary differential equations in reflexive Banach spaces. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (1978), 407–413.
MR 0492684 |
Zbl 0384.34039
[44] Szufla S.:
Sets of fixed points of nonlinear mappings in functions spaces. Funkcial. Ekvac. 22 (1979), 121–126.
MR 0551256
[45] Szufla S.:
On the application of measure of noncompactness to existence theorems. Rend. Sem. Mat. Univ. Padova 75 (1986), 1–14.
MR 0847653 |
Zbl 0589.45007