Approximation and Existence of Solutions to Ordinary Differential Equations in Banach Spaces

1 Ambrosetti, A. Un teorema di esistenza per le equazioni differenziali negli spazi di Banach Rend. Sem. Mat. Univ. Padova 39 1967 349-361 MR0222426

2 Bony, J. M. Principe du maximum, inégalité de Harnack et unicité du problemes de Cauchy pour les op6rateurs elliptiques dégénérés Ann. Inst. Fourier Grenoble 19 1969 277-304 MR0262881

3 Brezis, H. On a characterization of flow-invariant sets Comm. Pure App. Math. 23 1970 261-263 MR0257511

4 Browder, F. E. Non-linear equations of evolution Ann. of Math. 80 1964 485-523 MR0173960

5 Cellina, A. On the existence of solutions of ordinary differential equations in Banach spaces Funkcialaj Ekvacioj 14 1971 129-136 MR0304805 0304805

6 Cellina, A. On the local existence of solutions of ordinary differential equations Bull. Acad. Polon. Sci., Ser. Sci. Math. Astronom. Phys. 20 1972 293-296 MR0315237

7 Corduneanu, C. Equazioni differenziali negli spazi di Banach Teoremi di esistenza e prolungabilitz Rend. Acc. Naz. Lincei 23 1957 226-230 MR0096830

Crandall, M. G. Differential equations on convex sets J. Math. Soc. Japan 22 1970 443-455 MR0268491

9 Crandall, M. G. A generalization of Peano's existence theorem and flow invariance Proc. Amer. Math. Soc. 36 1972 151-155 MR0306586

10 Hartman, P. Generalized Lyapunov functions and functional equations Annali de Mat. Pura Appl. 69 1965 305-320 MR0192370

11 Hartman, P. On invariant sets and on a theorem of Wazewski Proc. Amer. Math. Soc. 32 1972 511-520 MR0298091

12 Kakutani, S. A generalization of Brouwer's fixed point theorem Duke Math. J. 8 1941 457-459 MR0004776

13 Kuratowski, K. Topology, Vol.I Academic Press, New York 1966 MR0217751

14 Lasota, A.; Yorke, J. A. The generic property of existence of solutions of differential equations in Banach spaces J. Diff. Eqns. 13 1973 1-12 MR0335994

15 Li, T. Y., Existence of solutions for ordinary differential equations in Banach spaces, (to appear) MR0369848

16 Martin, Jr., R. H. Lyapunov functions and autonomous differential equations in a Banach space Math. Systems Theory 7 1973 66-72 MR0322301

17 Martin, Jr., R. H. Differential equations on closed subsets of a Banach space Trans. Amer. Math. Soc. 179 1973 399-414 MR0318991

18 Murakami, H. On nonlinear ordinary and evolution equations Funkcialaj Ekvacioj 9 1966 151-162 MR0209617 0209617

19 Nagumo, M. Über die Laga der Integralkurven gewöhnlicher Differentialgleichungen Proc. Phys.-Math. Soc. Japan 24 1942 551-559 MR0015180

20 Nirenberg, L. Functional Analysis Courant Institute of Mathematical Sciences, New York University, New York 1961

21 Redheffer, R. M. The theorems of Bony and Brezis on flow invariant sets Amer. Math. Monthly 79 1972 740-747 MR0303024

22 Szufla, S. Some remarks on ordinary differential equations in Banach spaces Bull. Acad. Polon. Sci., Ser. Sci. Math. Astronom. Phys. 16 1968 795-800 MR0239238

23 Yorke, J. A. Invariance for ordinary differential equations Math. Systems Theory 1 1967 353-372 MR0226105

24 Yorke, J. A. Differential inequalities and non-Lipschitz scalar functions Math. Systems Theory 4 1970 140-153 MR0268476