Measures of noncompactness in the study of solutions of nonlinear differential and integral equations

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1. [1] Akhmerov R.R., Kamenskii M.I., Potapov A.S., Rodkina A.E., Sadovskii B.N., Measures of Noncompactness and Condensing Operators, Oper. Theory Adv. Appl., 55, Birkhäuser, Basel, 1992 
2. [2] Appell J., Banas J., Merentes N., Measures of noncompactness in the study of asymptotically stable and ultimately nondecreasing solutions of integral equations, Z. Anal. Anwend., 2010, 29(3), 251–273 http://dx.doi.org/10.4171/ZAA/1408[Crossref][WoS] Zbl1214.47044
3. [3] Ayerbe Toledano J.M., Domınguez Benavides T., López Acedo G., Measures of Noncompactness in Metric Fixed Point Theory, Oper. Theory Adv. Appl., 99, Birkhäuser, Basel, 1997 http://dx.doi.org/10.1007/978-3-0348-8920-9[Crossref] Zbl0885.47021
4. [4] Banaś J., Goebel K., Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Appl. Math., 60, Marcel Dekker, New York, 1980 Zbl0441.47056
5. [5] Banaś J., Lecko M., Solvability of infinite systems of differential equations in Banach sequence spaces, J. Comput. Appl. Math., 2001, 137(2), 363–375 http://dx.doi.org/10.1016/S0377-0427(00)00708-1[Crossref] Zbl0997.34048
6. [6] Banaś J., Olszowy L., Measures of noncompactness related to monotonicity, Comment. Math. Prace Mat., 2001, 41, 13–23 Zbl0999.47041
7. [7] Banaś J., Rzepka B., On existence and asymptotic behavior of solutions of infinite systems of differential equations, Panamer. Math. J., 2004, 14(1), 105–115 Zbl1053.34056
8. [8] Banas J., Rzepka B., Monotonic solutions of a quadratic integral equation of fractional order, J. Math. Anal. Appl., 2007, 332(2), 1371–1379 http://dx.doi.org/10.1016/j.jmaa.2006.11.008[Crossref] Zbl1123.45001
9. [9] Banas J., Zajac T., Solvability of a functional integral equation of fractional order in the class of functions having limits at infinity, Nonlinear Anal., 2009, 71(11), 5491–5500 http://dx.doi.org/10.1016/j.na.2009.04.037[Crossref] Zbl1181.45010
10. [10] Darbo G., Punti uniti in trasformazioni a codominio non compatto, Rend. Sem. Math. Univ. Padova, 1955, 24, 84–92 Zbl0064.35704
11. [11] Deimling K., Ordinary Differential Equations in Banach Spaces, Lecture Notes in Math., 596, Springer, Berlin-New York, 1977 Zbl0361.34050
12. [12] Dunford N., Schwartz J.T., Linear Operators I, Pure Appl. Math., 7, Interscience, New York-London, 1958 Zbl0084.10402
13. [13] Granas A., Dugundji J., Fixed Point Theory, Springer Monogr. Math., Springer, New York, 2003 Zbl1025.47002
14. [14] Kilbas A.A., Srivastava H.M., Trujillo J.J., Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud., 204, Elsevier, Amsterdam, 2006 http://dx.doi.org/10.1016/S0304-0208(06)80001-0[Crossref] 
15. [15] Maurin K., Analysis I, Biblioteka Matematyczna, 69, PWN, Warsaw, 1991 (in Polish) 
16. [16] Mazur S., Über die kleinste konvexe Menge, die eine gegebene kompakte Menge enthält, Studia Math., 1930, 2, 7–9 Zbl56.0091.01
17. [17] Mönch H., von Harten G.-F., On the Cauchy problem for ordinary differential equations in Banach spaces, Arch. Math. (Basel), 1982, 39(2), 153–160 http://dx.doi.org/10.1007/BF01899196[Crossref] 
18. [18] Mursaleen M., Mohiuddine S.A., Applications of measures of noncompactness to the infinite system of differential equations in l p spaces, Nonlinear Anal., 2012, 75(4), 2111–2115 http://dx.doi.org/10.1016/j.na.2011.10.011[Crossref] 
19. [19] Persidskiĭ K.P., Countable systems of differential equations and stability of their solutions, III, Izv. Akad. Nauk Kazah. SSR Ser. Fiz.-Mat. Nauk, 1961, 9, 11–34 (in Russian) 
20. [20] Podlubny I., Fractional Differential Equations, Math. Sci. Engrg., 198, Academic Press, San Diego, 1999 
21. [21] Valeev K.G., Zhautykov O.A., Infinite Systems of Differential Equations, Nauka Kazah. SSR, Alma-Ata, 1974 (in Russian)