Abstract
In this paper we shall study the solvability of discontinuous functional equations, and apply the so-obtained results to discontinuous implicit initial value problems in ordered Banach spaces. The proofs are based on fixed point results in ordered spaces proved recently by the author. A concrete example is solved to demonstrate the obtained results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Heikkilä, S.: Existence and comparison results for operator and di.erential equations in abstract space. J. Math. Anal. Appl., 274(2), 586–607 (2002)
Heikkilä, S.: Existence results for operator equations in abstract spaces and an application. J. Math. Anal. Appl., 292, 262–273 (2004)
Heikkilä, S., Lakshmikantham, V.: Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations, Marcel Deccer, Inc., New York, Basel, Hong Kong, 1994
Lindenstraus, J., Tzafriri, L.: Classical Banach Spaces II, Function Spaces, Springer-Verlag, Berlin, 1979
Carl, S., Heikkilä, S.: Nonlinear Differential Equations in Ordered Spaces, Chapman & Hall/CRC, London, 2000
Birkho., G.: Lattice Theory, Amer. Math. Soc. Publ., Vol XXV, Providence, Rhode Island, 1973
Carl, S., Heikkilä, S.: Existence of solutions for discontinuous functional equations and elliptic boundary value problems. Electronic J. Differential Equations, 61, 1–10 (2002)
Heikkilä, S.: A method to solve discontinuous boundary value problems. Proc. 3rd World Congress of Nonlinear Analysts, Nonlinear Anal., 47(4), 2387–2394, 2001
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Heikkilä, S. On the Solvability of Implicit Functional Equations with Applications to Discontinuous Differential Equations. Acta Math Sinica 22, 223–232 (2006). https://doi.org/10.1007/s10114-005-0558-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10114-005-0558-9