| Title:
|
Existence results for differential equations in Banach spaces (English) |
| Author:
|
Lee, John W. |
| Author:
|
O'Regan, Donal |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
2 |
| Year:
|
1993 |
| Pages:
|
239-251 |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper presents existence results for initial and boundary value problems for nonlinear differential equations in Banach spaces. (English) |
| Keyword:
|
existence |
| Keyword:
|
initial value problems |
| Keyword:
|
boundary value problems |
| Keyword:
|
abstract spaces |
| MSC:
|
34A10 |
| MSC:
|
34A12 |
| MSC:
|
34B15 |
| MSC:
|
34G10 |
| MSC:
|
34G20 |
| idZBL:
|
Zbl 0786.34069 |
| idMR:
|
MR1241733 |
| . |
| Date available:
|
2009-01-08T18:03:04Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118577 |
| . |
| Reference:
|
[1] Banas J., Goebel K.: Measures and Noncompactness in Banach Spaces.Dekker, New York, Basel, 1980. MR 0591679 |
| Reference:
|
[2] Bobisud L.E., O'Regan D.: Existence of solutions to some singular initial value problems.J. Math. Anal. Appl. 133 (1988), 135-149. Zbl 0646.34003, MR 0960387 |
| Reference:
|
[3] Dugundji J., Granas A.: Fixed Point Theory.Monographie Matematyczne, PNW Warszawa, 1982. Zbl 1025.47002 |
| Reference:
|
[4] Dunford N., Schwartz J.T.: Linear Operators Part I: General Theory.Interscience Publishers, New York, 1967. Zbl 0635.47001, MR 1009162 |
| Reference:
|
[5] 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. Zbl 0643.34015, MR 0948766 |
| Reference:
|
[6] 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. Zbl 0687.34009, MR 1103033 |
| Reference:
|
[7] 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 |
| Reference:
|
[8] Lee J.W., O'Regan D.: Nonlinear boundary value problems in Hilbert spaces.J. Math. Anal. Appl. 137 (1989), 59-69. Zbl 0672.34056, MR 0981923 |
| Reference:
|
[9] Lee J.W., O'Regan D.: Topological transversality: Applications to initial value problems.Ann. Polonici Math. 48 (1988), 31-36. Zbl 0674.34006, MR 0978675 |
| Reference:
|
[10] Lee J.W., O'Regan D.: Existence of solutions for nonlinear differential delay equations in Banach and Hilbert spaces.Nonlinear Analysis, to appear. |
| Reference:
|
[11] O'Farrell A., O'Regan D.: Existence results for initial and boundary value problems.Proc. Amer. Math. Society 110 (1990), 661-673. |
| Reference:
|
[12] 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. Zbl 0684.34063, MR 1002176 |
| Reference:
|
[13] O'Regan D.: Second and higher order systems of boundary value problems.J. Math. Anal. Appl. 15 (1991), 120-149. Zbl 0744.34024 |
| Reference:
|
[14] O'Regan D.: Boundary value problems for second and higher order differential equations.Proc. Amer. Math. Soc. 113 (1991), 761-776. Zbl 0742.34023, MR 1069295 |
| Reference:
|
[15] Martin R.H.: Nonlinear Operators and Differential Equations in Banach Spaces.Wiley, New York, 1976. Zbl 0333.47023, MR 0492671 |
| Reference:
|
[16] Wintner A.: The nonlocal existence problem for ordinary differential equations.Amer. J. Math. 67 (1945), 277-284. MR 0011858 |
| Reference:
|
[17] Yoshida K.: Functional Analysis.Springer Verlag, Berlin, 1965. |
| . |
