Bipotentials are non smooth mechanics tools, used to model various non associative multivalued constitutive laws of dissipative materials (friction contact, soils, cyclic plasticity of metals, damage). Given by a graph M representing a multivalued constitutive law, we state a simple necessary and sufficient condition for the existence of a bipotential b for which M is the set of (x, y) such tha...

Since the fundamental theory of variational inequality was founded in the 1960s, the variational inequality theory with applications has made powerful progress and has become an important part of nonlinear analysis. It has been applied intensively to mechanics, differential equation, cybernetics, quantitative economics, optimization theory, nonlinear programming, and so forth (see [2]). In virt...

Abstract In the present article, we introduce a new type of generalized multivalued orthogonal α - F contraction integral mappings in context metric spaces and establish some fixed point results. We construct an example to show existence this work. Our results substantially unify, generalize complement comparable existing literature. As application our results, derive periodic for single valued...

The existence of martingale selectors for a multivalued supermartin-gale with continuous parameter is proved.We also prove the weak regularity of multivalued supermartingales.Using the regularity of Banach-valued martingales,we show a multivalued supermartingale has a cadlag modiication under Kuratowski convergence. x1. Introduction Multivalued martingales and supermartingales with discrete par...

We discuss a model of a conformal p-brane interacting with the world volume metric and connection. The purpose of the model is to suggest a mechanism by which gravity coupled to p-branes leads to the formation of structure rather than homogeneity in spacetime. Furthermore, we show that the formation of structure is accompanied by the appearance of a multivalued cosmological constant, i.e., one ...

and Applied Analysis 3 Remark 1.6. The examples of weak relatively uniformly nonexpansive multivalued mapping can be found in Su 1 and Homaeipour and Razani 2 . Let E be a real Banach space, and let E∗ be the dual space of E. Let f be a bifunction from C × C to R. The equilibrium problem is to find x̂ ∈ C such that fx̂, y ≥ 0, ∀y ∈ C. 1.3 The set of solutions of 1.3 is denoted by EP f . Given a m...

Following Bojarski and Vekua, we have studied the Dirichlet problem $$ \underset{z\to \zeta }{\lim}\operatorname{Re}\ f(z)=\varphi \left(\zeta \right) as z ? ?, ? D, ? ?D, with continuous boundary data ?(?) in bounded domains D of complex plane ?, where f satisfies degenerate Beltrami equation {f}_{\overline{z}}=\mu (z){f}_z,\left|\mu (z)\right|<1 , a.e. D. Assuming that is an arbitrary simply ...

In a real separable Hilbert space, we consider nonautonomous evolution equations including time-dependent subdifferentials and their nonmonotone multivalued perturbations. In this paper, we treat the multivalued dynamical systems associated with time-dependent subdifferentials, in which the solution is not unique for a given initial state. In particular, we discuss the asymptotic behaviour of o...