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2012 | 10 | 6 | 2003-2011
Tytuł artykułu

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

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The aim of this paper is to make an overview of some existence results for nonlinear differential and integral equations. Those results were obtained by the author and his co-workers during last years with some help of the technique of measures of noncompactness and a fixed point theorem of Darbo type.
Wydawca
Czasopismo
Rocznik
Tom
10
Numer
6
Strony
2003-2011
Opis fizyczny
Daty
wydano
2012-12-01
online
2012-10-12
Twórcy
  • Department of Mathematics, Rzeszów University of Technology, Powstańców Warszawy 8, 35-959, Rzeszów, Poland, jbanas@prz.edu.pl
Bibliografia
  • [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] 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]
  • [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]
  • [4] Banaś J., Goebel K., Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Appl. Math., 60, Marcel Dekker, New York, 1980
  • [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]
  • [6] Banaś J., Olszowy L., Measures of noncompactness related to monotonicity, Comment. Math. Prace Mat., 2001, 41, 13–23
  • [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
  • [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]
  • [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]
  • [10] Darbo G., Punti uniti in trasformazioni a codominio non compatto, Rend. Sem. Math. Univ. Padova, 1955, 24, 84–92
  • [11] Deimling K., Ordinary Differential Equations in Banach Spaces, Lecture Notes in Math., 596, Springer, Berlin-New York, 1977
  • [12] Dunford N., Schwartz J.T., Linear Operators I, Pure Appl. Math., 7, Interscience, New York-London, 1958
  • [13] Granas A., Dugundji J., Fixed Point Theory, Springer Monogr. Math., Springer, New York, 2003
  • [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] Maurin K., Analysis I, Biblioteka Matematyczna, 69, PWN, Warsaw, 1991 (in Polish)
  • [16] Mazur S., Über die kleinste konvexe Menge, die eine gegebene kompakte Menge enthält, Studia Math., 1930, 2, 7–9
  • [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] 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] 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] Podlubny I., Fractional Differential Equations, Math. Sci. Engrg., 198, Academic Press, San Diego, 1999
  • [21] Valeev K.G., Zhautykov O.A., Infinite Systems of Differential Equations, Nauka Kazah. SSR, Alma-Ata, 1974 (in Russian)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0120-9
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