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O’Regan, D.

Weak solutions of ordinary differential equations in Banach spaces. (English) Zbl 0933.34068

Appl. Math. Lett. 12, No. 1, 101-105 (1999).
Summary: An existence result is presented for differential equations in Banach spaces relative to the weak topology.

Cited in 35 Documents

MSC:

34G20 Nonlinear differential equations in abstract spaces

Keywords:

weak solutions; ordinary differential equations
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\textit{D. O'Regan}, Appl. Math. Lett. 12, No. 1, 101--105 (1999; Zbl 0933.34068)
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References:

[1] Szep, A., Existence theorems for weak solutions of ordinary differential equations in reflexive Banach spaces, Studia Sci. Math. Hungar., 6, 197-203 (1971) · Zbl 0238.34100
[2] Cramer, E.; Lakshmikantham, V.; Mitchell, A. R., On the existence of weak solutions of differential equations in nonreflexive Banach spaces, Nonlinear Anal., 2, 169-177 (1978) · Zbl 0379.34041
[3] Bugajewski, D., On the existence of weak solutions of integral equations in Banach spaces, Comment. Math. Univ. Carolinae, 35, 35-41 (1994) · Zbl 0816.45012
[4] Cichoń, M., Weak solutions of differential equations in Banach spaces, Discuss. Mathematicae—Differential Inclusions, 15, 5-14 (1995) · Zbl 0829.34051
[5] Cichoń, M.; Kubiaczyk, I., Existence theorems for the Hammerstein integral equation, Discussiones Mathematicae—Differential Inclusions, 16, 171-177 (1996) · Zbl 0911.45009
[6] Mitchell, A. R.; Smith, C. K.L., An existence theorem for weak solutions of differential equations in Banach spaces, (Lakshmikantham, V., Nonlinear Equations in Abstract Spaces (1978), Academic Press), 387-404 · Zbl 0452.34054
[7] O’Regan, D., Integral equations in reflexive Banach spaces and weak topologies, (Proc. Amer. Math. Soc., 124 (1996)), 607-614 · Zbl 0844.45009
[8] O’Regan, D., Fixed point theory for weakly sequentially continuous mappings, Mathl. Comput. Modelling, 27, 5, 1-14 (1998) · Zbl 1185.34026
[9] D. O’Regan, Operator equations in Banach spaces relative to the weak topology, (to appear).; D. O’Regan, Operator equations in Banach spaces relative to the weak topology, (to appear). · Zbl 0918.47053
[10] De Blasi, F. S., On a property of the unit sphere in Banach spaces, Bull. Math. Soc. Sci. Math. Roum., 21, 259-262 (1977) · Zbl 0365.46015
[11] Kubiaczyk, I.; Szufla, S., Kneser’s theorem for weak solutions of ordinary differential equations in Banach spaces, Publ. Inst. Math., 46, 99-103 (1982), (Beograd) · Zbl 0516.34058
[12] Smith, C. K.L., Measure of nonconvergence and noncompactness, (Ph.D Thesis (1978), University of Texas at Arlington)
[13] Arino, O.; Gautier, S.; Penot, J. P., A fixed point theorem for sequentially continuous mappings with applications to ordinary differential equations, Funkc. Ekvac., 27, 273-279 (1984) · Zbl 0599.34008
[14] Geitz, R. F., Pettis integration, (Proc. Amer. Math. Soc., 82 (1981)), 81-86 · Zbl 0506.28007
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