Recently, the higher order averaging method for studying periodic solutions of both Lipschitz differential equations and discontinuous piecewise smooth was developed in terms Brouwer degree theory. Between equations, there is a huge class lacking analysis on existence solutions, namely continuous non-Lipschitz equations. In this paper, based coincidence theory nonlinear operator we perform (non...

Let E be a closed set in R, and suppose that there is a k ≥ 1 such that every x, y ∈ E can be connected by a rectifiable path in E with length ≤ k |x−y|. This condition is satisfied by chord-arc curves, Lipschitz manifolds of any dimension, and fractals like Sierpinski gaskets and carpets. Note that length-minimizing paths in E are chord-arc curves with constant k. A basic feature of this condi...

We propose a generalized Newton method for solving the system of nonlinear equations with linear complementarity constraints in the implicit or semi-implicit time-stepping scheme for differential linear complementarity systems (DLCS). We choose a specific solution from the solution set of the linear complementarity constraints to define a locally Lipschitz continuous right-hand-side function in...

‎this contribution mainly focuses on some aspects of lipschitz groups‎, ‎i.e.‎, ‎metrizable groups with lipschitz multiplication and inversion map‎. ‎in the main result it is proved that metric groups‎, ‎with a translation-invariant metric‎, ‎may be characterized as particular group objects in the category of metric spaces and lipschitz maps‎. ‎moreover‎, ‎up to an adjustment of the metric‎, ‎a...

We prove the interior Hölder continuity of weak solutions to parabolic systems ∂uj ∂t −Dαa α j (x, t, u,∇u) = 0 in Q (j = 1, . . . , N) (Q = Ω×(0, T ),Ω ⊂ R2), where the coefficients aj (x, t, u, ξ) are measurable in x, Hölder continuous in t and Lipschitz continuous in u and ξ.

We give necessary and sufficient condition for existence and uniqueness of L-solutions of reflected BSDEs with continuous barrier, generator monotone with respect to y and Lipschitz continuous with respect to z, and with data in L, p ≥ 1. We also prove that the solutions may be approximated by the penalization method.

Suppose that X is an arbitrary real Banach space and T : X → X is a Lipschitz continuous φ-strongly accretive operator or uniformly continuous φ-strongly accretive operator. We prove that under different conditions the three-step iteration methods with errors converge strongly to the solution of the equation Tx = f for a given f ∈ X.

We formally state and prove the wellposedness and the local Lipschitz continuity of the multisurface stress-strain law of nonlinear kinematic hardening type due to Chaboche within the space of time-dependent tensor-valued absolutely continuous functions. The results also include the more general case of a continuous family of auxiliary surfaces.

We consider a model for supply chains governed by partial differential equations. The mathematical properties of a continuous model are discussed and existence and uniqueness is proven. Moreover, Lipschitz continuous dependence on the initial data is proven. We make use of the front tracking method to construct approximate solutions. The obtained results extend the preliminary work of [12].