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On the behaviour of measures of noncompactness with respect to differentiation and integration of vector-valued functions. (English) Zbl 0528.47046


MSC:

47J25 Iterative procedures involving nonlinear operators
47H10 Fixed-point theorems
34G20 Nonlinear differential equations in abstract spaces

Citations:

Zbl 0418.34060
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Full Text: DOI

References:

[1] Banaś, J.; Goebel, K., Measures of noncompactness in Banach spaces, Lecture Notes pure Appl. Math., 60 (1980), New York, Basel · Zbl 0441.47056
[2] Deimling, K., On existence and uniqueness for Cauchy’s problem in infinite-dimensional Banach spaces, Proc. Colloqu. Math. Soc. Janos Bólyai, Vol. 15, 131-142 (1975), Diff. Eqs. · Zbl 0364.34030
[3] Deimling, K., Ordinary differential equations in Banach spaces, (Lecture Notes in Mathematics, 596 (1977), Springer: Springer Berlin) · Zbl 0555.60036
[4] Deimling, K., On some open problems for ordinary differential equations in Banach spaces, Equa-Diff, 78, 127-137 (1978) · Zbl 0418.34060
[5] Deimling, K., Fixed points of condensing maps, (Volterra equations, Proz. Symp. Otanemi, Finland 1978, 737 (1979), Springer: Springer New York), Lecture Notes in Mathematics · Zbl 0418.47030
[6] Deimling, K.; Lakshmikantham, V. V., On existence of extremal solutions of differential equations in Banach spaces, Nonlinear Analysis, 3, 563-568 (1979) · Zbl 0418.34061
[7] Deimling, K.; Larshmikantham, V. V., Existence and comparison theorems for differential equations in Banach spaces, Nonlinear Analysis, 3, 569-575 (1979) · Zbl 0418.34062
[8] Dugundji, J., An extension of Tietze’s theorem, Pacif. J. Math., 1, 353-367 (1951) · Zbl 0043.38105
[9] Edwards, R. E., Functional Analysis-Theory and Applications (1965), New York · Zbl 0182.16101
[10] Lakshmikantham, V. V., Existence and comparison results for Volterra integral equations in a Banach space, Voltera equations, Proc. Symp., Otanemi, Finland 1978, 737 (1979), Lecture Notes in Mathematics · Zbl 0418.45015
[11] Mönch, H., Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonlinear Analysis, 4, 985-999 (1980) · Zbl 0462.34041
[12] Mönch, H.; von Harten, G.-F., On the Cauchy problem for ordinary differential equations in Banach spaces, Arch. Math., 39, 153-160 (1982) · Zbl 0496.34033
[13] Sadovskij, B. N., Limit-compact and condensing operators, Russ. math. Survs, 27, 85-155 (1972) · Zbl 0243.47033
[14] Vaughn, R. L., Existence and comparison results for nonlinear Volterra integral equations in a Banach space, Applicable Analysis, 7, 337-348 (1977/1978) · Zbl 0403.45023
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