An extension of the linear complementarity problem (LCP) of mathematical programming is the so-called rational complementarity problem (RCP). This problem occurs if com-plementarity conditions are imposed on input and output variables of linear dynamical in-put/state/output systems. The resulting dynamical systems are called linear complementar-ity systems. Since the RCP is crucial both in issu...

An extension of the linear complementarity problem (LCP) of mathematical programming is the so-called rational complementarity problem (RCP). This problem occurs if complementarity conditions are imposed on input and output variables of linear dynamical input/state/output systems. The resulting dynamical systems are called linear complementarity systems. Since the RCP is crucial both in issues ...

This paper is an up-to-date introduction to the problem of uniqueness versus non-uniqueness of infinite clusters for percolation on Z d and, more generally, on transitive graphs. For iid percolation on Z, uniqueness of the infinite cluster is a classical result, while on certain other transitive graphs uniqueness may fail. Key properties of the graphs in this context turn out to be amenability ...

We present some fixed point results for a single mapping and a pair of compatible mappings via auxiliary functions which satisfy a generalized weakly contractive condition in partially ordered complete $G$-metric spaces. Some examples are furnished to illustrate the useability of our main results. At the end, an application is presented to the study of exi...

In this paper has been studied the wave equation in some non-classic cases. In the  rst case boundary conditions are non-local and non-periodic. At that case the associated spectral problem is a self-adjoint problem and consequently the eigenvalues are real. But the second case the associated spectral problem is non-self-adjoint and consequently the eigenvalues are complex numbers,in which two ...

We consider the exact controllability for the problem of transmission of the plate equation with lower-order terms. Using Lions’ Hilbert Uniqueness Method (HUM for short), we show that the system is exactly controllable in L(Ω) ×H−2(Ω) . We also obtain some uniqueness theorems for the problem of transmission of the plate equation and for the operator a(x)∆ + q .

A mixed finite element method combined with a fixed point algorithm is proposed for solving the thermally coupled quasi-Newtonian flow problem. The existence and uniqueness of the mixed variational solution are established. A more general uniqueness result for the original system problem is presented. The convergence of the approximate solution is analyzed and the corresponding error estimates ...