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Some fixed point theorems for multifunctions with applications in game theory

Būi Cong Cuōng — 1985

IntroductionThe main result of this paper is concerned with the conditions which guarantee that a multifunction f : C 2 X defined on an arbitrary subset C of a topological vector space X admits a point x of C such that x∈f(x).First, we give some definitions and propositions which are associated with semicontinuous multifunctions (Part 1).Next, in Part 2, we present a global convergence criterion on variable dimension algorithms for finding an approximate solution of the equation x∈f(x), and then we consider...

Nontrivial solutions to boundary value problems for semilinear Δ γ -differential equations

Duong Trong Luyen — 2021

Applications of Mathematics

In this article, we study the existence of nontrivial weak solutions for the following boundary value problem: - Δ γ u = f ( x , u ) in Ω , u = 0 on Ω , where Ω is a bounded domain with smooth boundary in N , Ω { x j = 0 } for some j , Δ γ is a subelliptic linear operator of the type Δ γ : = j = 1 N x j ( γ j 2 x j ) , x j : = x j , N 2 , where γ ( x ) = ( γ 1 ( x ) , γ 2 ( x ) , , γ N ( x ) ) satisfies certain homogeneity conditions and degenerates at the coordinate hyperplanes and the nonlinearity f ( x , ξ ) is of subcritical growth and does not satisfy the Ambrosetti-Rabinowitz (AR) condition.

On the hierarchy of functioning rules in distributed computing

A. BuiM. BuiC. Lavault — 2010

RAIRO - Operations Research

In previous papers, we used a Markovian model to determine the optimal functioning rules of a distributed system in various settings. Searching optimal functioning rules amounts to solve an optimization problem under constraints. The hierarchy of solutions arising from the above problem is called the “first order hierarchy”, and may possibly yield equivalent solutions. The present paper emphasizes a specific technique for deciding between two equivalent solutions, which establishes the “second...

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