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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:
47J25Iterative procedures (nonlinear operator equations)
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
34G20Nonlinear ODE in abstract spaces
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References:
[1] Banaś, J.; Goebel, K.: Measures of noncompactness in Banach spaces. Lecture notes pure appl. Math. 60 (1980)
[2] Deimling, K.: On existence and uniqueness for Cauchy’s problem in infinite-dimensional Banach spaces. Proc. colloqu. Math. soc. Janos bólyai 15, 131-142 (1975)
[3] Deimling, K.: Ordinary differential equations in Banach spaces. Lecture notes in mathematics 596 (1977) · Zbl 0361.34050
[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)
[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) · 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)
[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