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The Special Issue contains eleven accepted and published submissions to a Special Issue of the MDPI journal Axioms on the subject of “Nonlinear Dynamical Systems with Applications” [...]

In this paper, some novel conditions for the stability results for a class of fractional-order quasi-linear impulsive integro-differential systems with multiple delays is discussed. First, the existence and uniqueness of mild solutions for the considered system is discussed using contraction mapping theorem. Then, novel conditions for Mittag–Leffler stability (MLS) of the considered system are established by using well known mathematical techniques, and further, the two corollaries are deduced, which still gives some new results. Finally, an example is given to illustrate the applications of the results.

In this paper, we introduce and study a fractional elliptic obstacle system, which is composed of two elliptic inclusions with fractional (pi; qi)-Laplace operators, nonlocal functions, and multivalued terms. The weak solution of fractional elliptic obstacle system is formulated by a fully nonlinear coupled system driven by two nonlinear and nonmonotone variational inequalities with constraints. The nonemptiness and compactness of solution set in the weak sense are proved via employing a surjectivity theorem to the multivalued operators formulated by the sum of a multivalued pseudomonotone operator and a maximal monotone operator. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the stability analysis for a contaminant convection-reaction-diffusion model of the recovered fracturing fluid (RFFM, for short), which couples a nonlinear and non-smooth stationary incompressible Navier-Stokes equation with a multivalued frictional boundary condition, and a nonlinear reaction-diffusion equation with mixed Neumann boundary conditions. First, we introduce a family of perturbation problems corresponding to (RFFM), and present the variational formulation of perturbation problem which is a perturbation elliptic hemivariational inequality driven by a perturbation nonlinear variational equation. Then, the existence of solutions and the uniform bound of the solution set to the perturbation problem are obtained. Finally, it is established that, as the perturbation parameter tends to zero, the solution set of the perturbation problems converge to the solution set of (RFFM) in the sense of the Kuratowski upper limit. This shows that (RFFM) is stable with respect to the perturbation data. [ABSTRACT FROM AUTHOR]

In this paper we consider a class of double phase differential inclusions of the type {-div(|∇u|p-2∇u+μ(x)|∇u|q-2∇u)∈∂C²f(x,u),u=0, in Ω, on ∂Ω, where Ω⊂RN with N≥2 is a bounded domain with Lipschitz boundary, f(x,t) is measurable w.r.t. the first variable on Ω and locally Lipschitz w.r.t. the second variable and ∂C²f(x,⋅) stands for the Clarke subdifferential of t↦f(x,t). The variational formulation of the problem gives rise to a so-called hemivariational inequality and the corresponding energy functional is not differentiable, but only locally Lipschitz. We use nonsmooth critical point theory to prove the existence of at least one weak solution, provided the ∂C²f(x,⋅) satisfies an appropriate growth condition. [ABSTRACT FROM AUTHOR]

In this paper, we consider a mixed boundary value problem with a double phase partial differential operator, an obstacle effect and a multivalued reaction convection term. Under very general assumptions, an existence theorem for the mixed boundary value problem under consideration is proved by using a surjectivity theorem for multivalued pseudomonotone operators together with the approximation method of Moreau-Yosida. Then, we introduce a family of the approximating problems without constraints corresponding to the mixed boundary value problem. Denoting by S the solution set of the mixed boundary value problem and by Sn the solution sets of the approximating problems, we establish the following convergence relation ... where w-lim supn→∞ Sn and s-lim supsupn→∞ stand for the weak and the strong Kuratowski upper limit of Sn, respectively. [ABSTRACT FROM AUTHOR]

This paper is devoted to a generalized time-dependent variational-hemivariational inequality with history-dependent operators. First, we introduce a new concept of gap functions to the time-dependent variational-hemivariational inequality under consideration. Then, we consider a regularized function, which is proved to be a gap function of the inequality problem, and establish several important properties to the regularized function. Furthermore, an global error bound to the time-dependent variational-hemivariational inequality, which implicitly depends on the regularized gap function, is obtained. Finally, a quasi-static contact problem with the constitutive law involving a convex subdifferential inclusion and long memory effect is studied as an illustrative application. [ABSTRACT FROM AUTHOR]