On the existence of extremal solutions of a classical Nicoletti boundary value problem
by
Seppo Heikkilä
University of Oulu, Finland
Coauthors: Seppo Seikkala, University of Oulu, Finland

We shall consider the classical functional Nicoletti boundary value problem x'(t)=f(t, x), x_i(t_i)=y_i, where I is a real interval, A is a nonempty (index) set, y_i belongs to an ordered Banach space X, F is the Banach space of all bounded functions from A into X with the sup-norm and the mapping f from I×C(I, F) into F is such that f(t, x) is strongly measurable in t and monotone in x with respect to a partial order of F. Existence of extremal solutions will be obtained without any continuity assumptions on f. Existence and uniqueness of solutions have been studied in [1] - [3], for example, with stronger assumptions on f.

References

[1] J. Blaz and W. Walter, Über Funktional-Differentialgleichungen mit voreilendem Argument, Mh.Math. 82, 1-16 (1976).

[2] S. Seikkala, On a Classical Nicoletti Boundary Value Problem, Mh.Math. 93, 225-238 (1982) .

[3] S. Heikkilä and S. Seikkala, On a Classical Nicoletti Boundary Value Problem with a Discontinuous Nonlinearity, Dynamic Systems and Applications 2, 501-506 (1996).

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Date received: May 26, 2005

Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caqw-90.