In this paper, a nonlinear alternative for multivalued maps is used to investigate the existence of solutions of first order impulsive initial value problem for differential inclusions in Banach spaces.

Subalgebras of germs of vector fields leaving $0$ fixed in ${R}^{2n}$, of finite codimension in symplectic Lie algebra contain the ideal of germs infinitely flat at $0$. We give an application.

We present some existence results for boundary value problems for first order multivalued differential systems. Our approach is based on topological transversality arguments, fixed point theorems and differential inequalities.

We investigate the existence of solutions to first order initial value problems for differential inclusions subject to impulsive effects. We shall rely on a fixed point theorem for condensing maps to prove our results.

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