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On some solutions of nonlocal Cauchy problems

Cichoń M., Majcher P.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2003

[Z] 43(2)

185-199

The aim of the paper is to give a theorem about the existence of solutions of a semilinear nonlocal Cauchy problem for ordinary differential equations in Banach spaces. Since all assumptions are expressed in terms of the weak topology, we obtain the existence of pseudo-integral-solutions instead of integral, Caratheodory or classical ones considered in previous papers.