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On bounded pseudo and weak solutions of a nonlinear differential equation in Banach spaces

Krzyśka S., Kubiaczyk I.

Demonstratio Mathematica

1999

Vol. 32, nr 2

323-330

In this paper, we prove an existence theorem for bounded pseudo and weak solution of the differential equation . XI(t) = A(t)x(t) + f(t, X(t)) where f(., X(.) ) is Pettis- integrable for each strongly absolutely continuous function X and f(t,.) is weakly-weakly sequentially continuous. We also assume some condition expressed in terms of De Blasi's measure of weak noncompactness.