Previous |  Up |  Next

Article

Keywords:
existence; initial value problems; boundary value problems; abstract spaces
Summary:
This paper presents existence results for initial and boundary value problems for nonlinear differential equations in Banach spaces.
References:
[1] Banas J., Goebel K.: Measures and Noncompactness in Banach Spaces. Dekker, New York, Basel, 1980. MR 0591679
[2] Bobisud L.E., O'Regan D.: Existence of solutions to some singular initial value problems. J. Math. Anal. Appl. 133 (1988), 135-149. MR 0960387 | Zbl 0646.34003
[3] Dugundji J., Granas A.: Fixed Point Theory. Monographie Matematyczne, PNW Warszawa, 1982. Zbl 1025.47002
[4] Dunford N., Schwartz J.T.: Linear Operators Part I: General Theory. Interscience Publishers, New York, 1967. MR 1009162 | Zbl 0635.47001
[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. MR 0948766 | Zbl 0643.34015
[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. MR 1103033 | Zbl 0687.34009
[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
[8] Lee J.W., O'Regan D.: Nonlinear boundary value problems in Hilbert spaces. J. Math. Anal. Appl. 137 (1989), 59-69. MR 0981923 | Zbl 0672.34056
[9] Lee J.W., O'Regan D.: Topological transversality: Applications to initial value problems. Ann. Polonici Math. 48 (1988), 31-36. MR 0978675 | Zbl 0674.34006
[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.
[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. MR 1002176 | Zbl 0684.34063
[13] O'Regan D.: Second and higher order systems of boundary value problems. J. Math. Anal. Appl. 15 (1991), 120-149. Zbl 0744.34024
[14] O'Regan D.: Boundary value problems for second and higher order differential equations. Proc. Amer. Math. Soc. 113 (1991), 761-776. MR 1069295 | Zbl 0742.34023
[15] Martin R.H.: Nonlinear Operators and Differential Equations in Banach Spaces. Wiley, New York, 1976. MR 0492671 | Zbl 0333.47023
[16] Wintner A.: The nonlocal existence problem for ordinary differential equations. Amer. J. Math. 67 (1945), 277-284. MR 0011858
[17] Yoshida K.: Functional Analysis. Springer Verlag, Berlin, 1965.
Partner of
EuDML logo