Existence and uniqueness of solutions for a general nonlinear variational inequality

AbstractIn this paper, two existence and uniquenss theorems of solutions for a general nonlinear variational inequality under reflexive Banach space settings are proved

Condensation and Evaporation of Mutually Repelling Particles :Steady states and limit cycles

We study condensation and evaporation of particles which repel each other, using a simple set of rules on a square lattice. Different results are obtained for a mobile and an immobile surface layer.A two point limit cycle is observed for high temperature and low pressure in both cases. Here the coverage oscillates between a high and a low value without ever reaching a steady state. The results for the immobile case depend in addition on the initial coverage.Comment: 8 pages, 3 figure

A selection and a fixed point theorem and an equilibrium point of an abstract economy

A selection theorem and a fixed point theorem are proved. The fixed point theorem is then applied to prove the existence of an equilibrium point of an abstract economy

Equilibrium points of random generalized games

In this paper, the concepts of random maximal elements, random equilibria and random generalized games are described. Secondly by measurable selection theorem, some existence theorems of random maximal elements for Lc-majorized correspondences are obtained. Then we prove existence theorems of random equilibria for non-compact one-person random games. Finally, a random equilibrium existence theorem for non-compact random generalized games (resp., random abstract economics) in topological vector spaces and a random equilibrium existence theorem of non-compact random games in locally convex topological vector spaces in which the constraint mappings are lower semicontinuous with countable number of players (resp., agents) are given. Our results are stochastic versions of corresponding results in the recent literatures

Bifurcation for the solutions of equations involving set valued mappings

This paper is devoted to a generalization of the bifurcation theorem of Karsnosel'skii and Rabinowitz to the set valued situation

Percolation in Models of Thin Film Depositions

We have studied the percolation behaviour of deposits for different (2+1)-dimensional models of surface layer formation. The mixed model of deposition was used, where particles were deposited selectively according to the random (RD) and ballistic (BD) deposition rules. In the mixed one-component models with deposition of only conducting particles, the mean height of the percolation layer (measured in monolayers) grows continuously from 0.89832 for the pure RD model to 2.605 for the pure RD model, but the percolation transition belong to the same universality class, as in the 2- dimensional random percolation problem. In two- component models with deposition of conducting and isolating particles, the percolation layer height approaches infinity as concentration of the isolating particles becomes higher than some critical value. The crossover from 2d to 3d percolation was observed with increase of the percolation layer height.Comment: 4 pages, 5 figure