Vector network equilibrium problems with capacity constraints of arcs and nonlinear scalarization methods

In this paper, a vector network equilibrium problem with capacity constraints of arcs is studied. By virtue of Fan-Browder’ fixed point theorem, an existence result of a (weak) vector equilibrium flow is derived. By using nonlinear scalarization methods, some sufficient and necessary conditions for a weak vector equilibrium flow are obtained.     

The existence of multiple equilibrium points in a global attractor for some p-Laplacian equation

In this paper, we are mainly concerned with some properties of the global attractor for some p-Laplacian equation with a Lyapunov function in a Banach space. Under some suitable assumptions, we prove the existence of multiple equilibrium points in a global attractor for some p-Laplacian equation.     

Techniques to generate hyper-ideals of multilinear operators

The usual techniques to generate ideals of multilinear operators between Banach spaces fail in generating hyper-ideals in general. In this paper, we fill this gap by developing two techniques to generate hyper-ideals of multilinear operators. The techniques we develop generate new classes of multilinear operators and show that some important well-studied classes are Banach or p-Banach hyper-ideals.     

Endomorphisms of free modules as sums of four quadratic endomorphisms

We will prove that every endomorphism of a free right R-module of infinite rank can be decomposed as a sum of four endomorphisms which satisfy some fixed polynomial identities.