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Existence of solutions for generalized differential equations with unbounded right-hand side. (English) Zbl 0582.34002
This paper is concerned with the existence of solutions to the initial value problem for generalized differential equations (orientor fields) when the right-hand side, F(t,x), may be unbounded. Two global and one local existence theorems are established when F satisfies Carathéodory type conditions involving weak integral boundedness conditions. The multiple-valued function F(t,\(\cdot)\) is assumed to have closed graph and to be lower semicontinuous at each point x where F(t,x) is not convex.

MSC:
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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