in this article we consider the averaging method for differential inclusions with fuzzy right-hand side for the case when the limit of a method of an average does not exist.

For an arbitrary second-order stable matrix A, we calculate the maximum positive value R for which the differential inclusion ẋ ∈ FR(x) := {(A +∆)x,∆ ∈ R2×2, ‖∆‖ ≤ R} is asymptotically stable.

In this paper we shall establish a result concerning the covering dimension of a set of the type {x ∈ X : Φ(x)∩Ψ(x) 6= ∅}, where Φ, Ψ are two multifunctions from X into Y and X, Y are real Banach spaces. Moreover, some applications to the differential inclusions will be given.

Generalised multivalued inequalities are studied in this paper. Our results enable us to discuss control problems and differential inclusions on proximate retracts.

*Correspondence: [email protected] 1Department of Applied Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an, 710121, China Full list of author information is available at the end of the article Abstract This study aims to explore modular inequalities of interval-valued fuzzy soft sets characterized by Jun’s soft J-inclusions. Using soft product operations...

Forward viability and invariance of time-dependent differential inclusions are studied with the aid of generalized differentials. Contingent derivative is compared with a newer concept of generalized differential quotient. It is shown that the latter is more suitable for expressing criteria of viability and invariance, as it better describes the directions tangent to invariant trajectories of d...

We prove local and global invertibility of Sobolev solutions of certain differential inclusions which prevent the differential matrix from having negative eigenvalues. Our results are new even for quasiregular mappings in two dimensions.

In this work, the authors study the existence of solutions for fractional differential inclusions in the sense of Almgren with Riemann-Liouville derivative. They also show the compactness of the solution set. A Peano type existence theorem is also proved.

Some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p–Laplacian.

We discuss the existence of solutions, u ∈ φ+W 1,∞ 0 (Ω;R), for differential inclusions of the form Du(x) ∈ E, a.e. in Ω . 1 – Introduction In this article we discuss the existence of solutions, u ∈ W 1,∞(Ω;Rm), for the Dirichlet problem involving differential inclusions of the form