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Extremality and comparison results for discontinuous third order functional initial-boundary value problems. (English) Zbl 0976.34009
The authors prove the existence of the extremal solutions to a class of initial-boundary value problems for third-order differential equations with functional dependence, which may involve discontinuous nonlinearities. Some theoretical examples are given to illustrate the main results.
Reviewer: Eduardo Liz (Vigo)

34A36 Discontinuous ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
Full Text: DOI
[1] A. Cabada, and, S. Heikkilä, Uniqueness, comparison and existence results for third order functional initial-boundary value problems, Comput. Math. Appl, to appear. · Zbl 0991.34015
[2] Cabada, A.; Lois, S., Existence of solution for discontinuous third order boundary value problems, J. comput. appl. math., 110, 105-114, (1999) · Zbl 0936.34015
[3] Carl, S.; Heikkilä, S., Nonlinear differential equations in ordered spaces, (2000), Chapman & Hall, London/New York and CRC, Boca Raton, FL · Zbl 0948.34001
[4] Hassan, E.R.; Rzymowski, W., Extremal solutions of a discontinuous differential equation, Nonlinear anal., 37, 997-1017, (1999) · Zbl 0949.34005
[5] Heikkilä, S.; Lakshmikantham, V., Monotone iterative techniques for discontinuous nonlinear differential equations, (1994), Dekker New York · Zbl 0804.34001
[6] Pouso, R.L., Upper and lower solutions for first-order discontinuous ordinary differential equations, J. math. anal. appl., 244, 466-482, (2000) · Zbl 0962.34008
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