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Second order dynamic inclusions. (English) Zbl 1126.34313

Summary: The theory of dynamic inclusions on a time scale is introduced, hence accommodating the special cases of differential inclusions and difference inclusions. Fixed point theory for set-valued upper semicontinuous maps, Green’s functions, and upper and lower solutions are used to establish existence results for solutions of second order dynamic inclusions.

MSC:

34A60 Ordinary differential inclusions
39A10 Additive difference equations
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References:

[1] Agarwal R P Meehan M O’Regan DFixed point theory and applications, Cambridge Tracts in Mathematics141, Cambridge University Press, Cambridge, 2001
[2] Agarwal R P O’Regan D Wong P J YPositive solutions of differential, difference and integral equations, Kluwer Academic Publishers, Dordrecht, 1999
[3] Bohner M Peterson ADynamic equations on time scales: an introduction with applications, Birkhäuser, Boston, 2001 · Zbl 0978.39001
[4] Bohner M Peterson AAdvances in dynamic equations on time scales, Birkhäuser, Boston, 2003 · Zbl 1025.34001
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