References
J. Banas and K. Goebel,Measures of Noncompactness in Banach Spaces, Marcel Dekker (New York, Basel, 1980).
J. Chandra, V. Lakshmikantham and A. R. Mitchell, Existence of solutions of boundary value problems for second order systems in Banach spaces,Nonl. Anal.,2 (1978), 157–168.
K. Deimling,Ordinary Differential Equations in Banach Spaces, Springer-Verlag (New York, Heidelberg and Berlin, 1977).
J. Dugundji and A. Granas,Fixed Point Theory, Monographie Matematyczne, PNW (Warszawa, 1982).
M. Frigon and J. W. Lee, Existence principles for Carathéodory differential equations in Banach spaces,Top. Methods in Nonlinear Anal.,1 (1993), 91–106.
A. Granas, R. B. Guenther and J. W. Lee, Some general existence principles in the Carathéodory theory of nonlinear differential systems,Jour. Math. Pures Appl.,70 (1991), 153–196.
W. Krawcewicz, Contribution a la theorie des equations nonlineaires dan les espaces de Banach,Dissertationes Matematicae,273 (1988).
V. Lakshmikantham and S. Leela,Nonlinear Differential Equations in Abstract Spaces, Pergamon Press (New York, 1981).
J. W. Lee and D. O'Regan, Nonlinear boundary value problems in Hilbert spaces,Jour. Math. Anal. Appl.,137 (1989), 59–69.
J. W. Lee and D. O'Regan, Existence results for differential equations in Banach spaces,Comment. Math. Univ. Carolinae,34 (1993), 239–251.
R. H. Martin Jr.,Nonlinear Operators and Differential Equations in Banach Spaces, John Wiley and Sons (New York, 1976).
J. Mawhin and M. Willem, Periodic solutions of some nonlinear second order differential equations in Hilbert spaces,Recent Advances in Differential Equations (Trieste, 1981), 287–293.
J. Mawhin, Two point boundary value problems for nonlinear second order differential equations in Hilbert spaces,Tokoku Math. Jour.,32 (1980), 225–233.
H. Mönch, Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces,Nonl. Anal.,4 (1980), 985–999.
D. O'Regan, A note on the application of topological transversality to nonlinear differential equations in Hilbert spaces,Rocky Moun. Journ. Math.,18 (1988), 801–811.
D. O'Regan, Compact self adjoint operators and existence of solutions to singular nonlinear boundary value problems in a real Hilbert space,Libertas Mathematica,13 (1993), 47–68.
R. Precup, Nonlinear boundary value problems for infinite systems of second order functional differential equations,“Babes-Bolyai” Univ., Seminar on Differential Equations, Preprint number8 (1988), 17–30.
B. N. Sadovski, A fixed point principle,Funct. Anal. Appl.,1 (1967), 151–153.
K. Schmitt and R. Thompson, Boundary value problems for infinite systems of second order differential equations,Jour. Diff. Eq.,18 (1975), 277–195.
D. R. Smart,Fixed Point Theorems, Cambridge Tracts in Math.,66 (London, 1974).
W. Walter, Existence theorems for a two point boundary value problem in Banach spaces,Math. Ann.,244 (1979), 55–64.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
O'Regan, D. Measures of noncompactness, darbo maps and differential equations in abstract spaces. Acta Math Hung 69, 233–261 (1995). https://doi.org/10.1007/BF01876228
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01876228