Existence results for differential equations in Banach spaces
Lee, John W. ; O'Regan, Donal
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993), p. 239-251 / Harvested from Czech Digital Mathematics Library

This paper presents existence results for initial and boundary value problems for nonlinear differential equations in Banach spaces.

Publié le : 1993-01-01
Classification:  34A10,  34A12,  34B15,  34G10,  34G20
@article{118577,
     author = {John W. Lee and Donal O'Regan},
     title = {Existence results for differential equations in Banach spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {34},
     year = {1993},
     pages = {239-251},
     zbl = {0786.34069},
     mrnumber = {1241733},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118577}
}
Lee, John W.; O'Regan, Donal. Existence results for differential equations in Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 239-251. http://gdmltest.u-ga.fr/item/118577/

Banas J.; Goebel K. Measures and Noncompactness in Banach Spaces, Dekker, New York, Basel, 1980. | MR 0591679

Bobisud L.E.; O'Regan D. Existence of solutions to some singular initial value problems, J. Math. Anal. Appl. 133 (1988), 135-149. (1988) | MR 0960387 | Zbl 0646.34003

Dugundji J.; Granas A. Fixed Point Theory, Monographie Matematyczne, PNW Warszawa, 1982. | Zbl 1025.47002

Dunford N.; Schwartz J.T. Linear Operators Part I: General Theory, Interscience Publishers, New York, 1967. | MR 1009162 | Zbl 0635.47001

Frigon M.; Granas A.; Guennoun Z. Sur l'intervalle maximal d'existence de solutions pour des inclusions différentielles, C.R. Acad. Sci., Paris 306 (1988), 747-750. (1988) | MR 0948766 | Zbl 0643.34015

Granas A.; Guenther R.B.; Lee J.W. Some general existence principles in the Carathéodory theory of nonlinear differential systems, J. Math. Pures Appl. 70 (1991), 153-196. (1991) | MR 1103033 | Zbl 0687.34009

Granas A.; Guenther R.B.; Lee J.W. Existence principles for classical and Carathéodory solutions for systems of ordinary differential equations, Proc. Inter. Conf. on Theory and Appl. of Diff. Eq., Ohio Univ. Press, Athens, Ohio, 1988, 353-364. | MR 1026162

Lee J.W.; O'Regan D. Nonlinear boundary value problems in Hilbert spaces, J. Math. Anal. Appl. 137 (1989), 59-69. (1989) | MR 0981923 | Zbl 0672.34056

Lee J.W.; O'Regan D. Topological transversality: Applications to initial value problems, Ann. Polonici Math. 48 (1988), 31-36. (1988) | MR 0978675 | Zbl 0674.34006

Lee J.W.; O'Regan D. Existence of solutions for nonlinear differential delay equations in Banach and Hilbert spaces, Nonlinear Analysis, to appear.

O'Farrell A.; O'Regan D. Existence results for initial and boundary value problems, Proc. Amer. Math. Society 110 (1990), 661-673. (1990)

O'Regan D. A note on the application of topological transversality to nonlinear differential equations in Hilbert spaces, Rocky Mountain J. Math. 18 (1988), 801-811. (1988) | MR 1002176 | Zbl 0684.34063

O'Regan D. Second and higher order systems of boundary value problems, J. Math. Anal. Appl. 15 (1991), 120-149. (1991) | Zbl 0744.34024

O'Regan D. Boundary value problems for second and higher order differential equations, Proc. Amer. Math. Soc. 113 (1991), 761-776. (1991) | MR 1069295 | Zbl 0742.34023

Martin R.H. Nonlinear Operators and Differential Equations in Banach Spaces, Wiley, New York, 1976. | MR 0492671 | Zbl 0333.47023

Wintner A. The nonlocal existence problem for ordinary differential equations, Amer. J. Math. 67 (1945), 277-284. (1945) | MR 0011858

Yoshida K. Functional Analysis, Springer Verlag, Berlin, 1965.