### Filippov's theorem for impulsive differential inclusions with fractional order.

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In this paper, we use the extrapolation method combined with a recent nonlinear alternative of Leray-Schauder type for multivalued admissible contractions in Fréchet spaces to study the existence of a mild solution for a class of first order semilinear impulsive functional differential inclusions with finite delay, and with operator of nondense domain in original space.

In this paper, we study ϕ-Laplacian problems for differential inclusions with Dirichlet boundary conditions. We prove the existence of solutions under both convexity and nonconvexity conditions on the multi-valued right-hand side. The nonlinearity satisfies either a Nagumo-type growth condition or an integrably boundedness one. The proofs rely on the Bonhnenblust-Karlin fixed point theorem and the Bressan-Colombo selection theorem respectively. Two applications to a problem from control theory are...

We prove the existence of solutions of differential inclusions on a half-line. Our results are based on an approximation method combined with a diagonalization method.

In this paper we discuss the existence of oscillatory and nonoscillatory solutions of first order impulsive differential inclusions. We shall rely on a fixed point theorem of Bohnenblust-Karlin combined with lower and upper solutions method.

We study the existence of solutions for random system of fractional differential equations with boundary nonlocal initial conditions. Our approach is based on random fixed point principles of Schaefer and Perov, combined with a vector approach that uses matrices that converge to zero. We prove existence and uniqueness results for these systems. Some examples are presented to illustrate the theory.

In this paper we investigate the existence of multiple positive solutions for nonlinear boundary value problems with integral boundary conditions. We shall rely on the Leggett-Williams fixed point theorem.

In this paper a fixed point theorem due to Covitz and Nadler for contraction multivalued maps, and the Schaefer’s theorem combined with a selection theorem due to Bressan and Colombo for lower semicontinuous multivalued operators with decomposables values, are used to investigate the existence of solutions for boundary value problems of fourth-order differential inclusions.

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