Existence results for differential equations in Banach spaces

John W. Lee; Donal O'Regan

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 2, page 239-251
  • ISSN: 0010-2628

Abstract

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

How to cite

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Lee, John W., and O'Regan, Donal. "Existence results for differential equations in Banach spaces." Commentationes Mathematicae Universitatis Carolinae 34.2 (1993): 239-251. <http://eudml.org/doc/247469>.

@article{Lee1993,
abstract = {This paper presents existence results for initial and boundary value problems for nonlinear differential equations in Banach spaces.},
author = {Lee, John W., O'Regan, Donal},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {existence; initial value problems; boundary value problems; abstract spaces; existence; ordinary differential equations in Banach spaces; Cauchy problem; two-point boundary-value problem; compactness},
language = {eng},
number = {2},
pages = {239-251},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Existence results for differential equations in Banach spaces},
url = {http://eudml.org/doc/247469},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Lee, John W.
AU - O'Regan, Donal
TI - Existence results for differential equations in Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 2
SP - 239
EP - 251
AB - This paper presents existence results for initial and boundary value problems for nonlinear differential equations in Banach spaces.
LA - eng
KW - existence; initial value problems; boundary value problems; abstract spaces; existence; ordinary differential equations in Banach spaces; Cauchy problem; two-point boundary-value problem; compactness
UR - http://eudml.org/doc/247469
ER -

References

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  1. Banas J., Goebel K., Measures and Noncompactness in Banach Spaces, Dekker, New York, Basel, 1980. MR0591679
  2. Bobisud L.E., O'Regan D., Existence of solutions to some singular initial value problems, J. Math. Anal. Appl. 133 (1988), 135-149. (1988) Zbl0646.34003MR0960387
  3. Dugundji J., Granas A., Fixed Point Theory, Monographie Matematyczne, PNW Warszawa, 1982. Zbl1025.47002
  4. Dunford N., Schwartz J.T., Linear Operators Part I: General Theory, Interscience Publishers, New York, 1967. Zbl0635.47001MR1009162
  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. (1988) Zbl0643.34015MR0948766
  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. (1991) Zbl0687.34009MR1103033
  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. MR1026162
  8. Lee J.W., O'Regan D., Nonlinear boundary value problems in Hilbert spaces, J. Math. Anal. Appl. 137 (1989), 59-69. (1989) Zbl0672.34056MR0981923
  9. Lee J.W., O'Regan D., Topological transversality: Applications to initial value problems, Ann. Polonici Math. 48 (1988), 31-36. (1988) Zbl0674.34006MR0978675
  10. Lee J.W., O'Regan D., Existence of solutions for nonlinear differential delay equations in Banach and Hilbert spaces, Nonlinear Analysis, to appear. 
  11. O'Farrell A., O'Regan D., Existence results for initial and boundary value problems, Proc. Amer. Math. Society 110 (1990), 661-673. (1990) 
  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. (1988) Zbl0684.34063MR1002176
  13. O'Regan D., Second and higher order systems of boundary value problems, J. Math. Anal. Appl. 15 (1991), 120-149. (1991) Zbl0744.34024
  14. O'Regan D., Boundary value problems for second and higher order differential equations, Proc. Amer. Math. Soc. 113 (1991), 761-776. (1991) Zbl0742.34023MR1069295
  15. Martin R.H., Nonlinear Operators and Differential Equations in Banach Spaces, Wiley, New York, 1976. Zbl0333.47023MR0492671
  16. Wintner A., The nonlocal existence problem for ordinary differential equations, Amer. J. Math. 67 (1945), 277-284. (1945) MR0011858
  17. Yoshida K., Functional Analysis, Springer Verlag, Berlin, 1965. 

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