Solutions For Second-order Differential Inclusions Research Articles

Existence of solutions for second-order differential inclusions involving proximal normal cones

In this work, we prove global existence of solutions for second-order differential problems in a general framework. More precisely, we consider second-order differential inclusions involving proximal normal cone to a set-valued map. This set-valued map is supposed to take admissible values (so in particular uniformly prox-regular values, which may be non-smooth and non-convex). Moreover the solution is required to satisfy an impact law, appearing in the description of mechanical systems with inelastic shocks.

Existence solutions for second-order differential inclusions with nonconvex perturbations

The article studies the three-point boundary value problems for second-order perturbed differential inclusions of the form a.e. on [0,1]. The existence of solutions is proved under nonconvexity condition for the multifunction H.

Upper and lower solutions method for differential inclusions with integral boundary conditions

A nonlinear alternative of the Leray-Schauder type for multivalued maps combined with upper and lower solutions is used to investigate the existence of solutions for second-order differential inclusions with integral boundary conditions.