We prove the existence of viable solutions to the Cauchy problem x” ∈ F(x,x’), x(0) = x₀, x’(0) = y₀, where F is a set-valued map defined on a locally compact set , contained in the Fréchet subdifferential of a ϕ-convex function of order two.
We study an optimization problem given by a discrete inclusion with end point constraints. An approach concerning second-order optimality conditions is proposed.
We study a class of nonconvex Hadamard fractional integral inclusions and we establish some Filippov type existence results.
We consider a nonconvex and nonclosed Sturm-Liouville type differential inclusion and we prove the arcwise connectedness of the set of its solutions.
We consider a class of nonconvex and nonclosed hyperbolic differential inclusions and we prove the arcwise connectedness of the solution set.
We establish several variational inclusions for solutions of a nonconvex Sturm-Liouville type differential inclusion on a separable Banach space.
We consider a nonlinear differential inclusion defined by a set-valued map with nonconvex values and we prove that the reachable set of a certain variational inclusion is a derived cone in the sense of Hestenes to the reachable set of the initial differential inclusion. In order to obtain the continuity property in the definition of a derived cone we use a continuous version of Filippov's theorem for solutions of our differential inclusion. As an application, in finite dimensional spaces, we obtain...
We consider a Cauchy problem associated to a second-order evolution inclusion in non separable Banach spaces under Filippov type assumptions and we prove the existence of mild solutions.
A certain converse statement of the Filippov-Wažewski theorem is proved. This result extends to the case of time dependent differential inclusions a previous result of Jo’o and Tallos in [5] obtained for autonomous differential inclusions.
We consider a nonconvex integral inclusion and we prove a Filippov type existence theorem by using an appropiate norm on the space of selections of the multifunction and a contraction principle for set-valued maps.
We consider a boundary value problem for first order nonconvex differential inclusion and we obtain some existence results by using the set-valued contraction principle.
We consider a nonconvex and nonclosed second-order evolution inclusion and we prove the arcwise connectedness of the set of its mild solutions.
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