This paper is devoted to the study of a perturbed differential inclusion governed by a sweeping process in a Hilbert space. The sweeping process is perturbed by a sum of a single-valued map satisfying a Lipschitz condition ...

In the paper, the set-valued covering mappings are studied. The statements on solvability, solution estimates, and well-posedness of inclusions with conditionally covering mappings are proved. The results obtained are ...

We study a singularly perturbed problem related to infinity Laplacian operator with prescribed boundary values in a region. We prove that solutions are locally (uniformly) Lipschitz continuous, they grow as a linear function, ...

We give new criteria for weak and strong invariant closed sets for differential inclusions in Double-struck capital Rn, and which are simultaneously governed by Lipschitz Cusco mapping and by maximal monotone operators. ...

This paper is devoted to the study of a nonconvex perturbed sweeping process with time delay in the infinite dimensional setting. On the one hand, the moving subset involved is assumed to be prox-regular and to move in an ...

In this work we use the stochastic flow decomposition technique to get components that represent the dynamics of the slow and fast motion of a stochastic differential equation with a random perturbation. Assuming a Lipschitz ...

We present results for the following singular perturbation problem: ∆p(x)uε := div(|∇uε(x)| p(x)−2∇uε) = βε(uε) + f ε, uε ≥ 0 (Pε(f ε)) in Ω ⊂ RN , where ε > 0, βε(s) = 1 εβ( s ε ), with β a Lipschitz function satisfying ...