Sentence examples for problem of equilibria from inspiring English sources

The global-stability problem of equilibria is investigated for coupled systems of differential equations on networks.

The global-stability problem of equilibria has been investigated for coupled systems of differential equations on networks for many years [1 6].

Although the problem of equilibria with magnetic islands is two dimensional, for small islands the numerical stability of the simple iteration may be analyzed using a one-dimensional equation similar to the linearized equilibrium equation used to analyze physical (resistive) instability.

In this paper, we introduce and analyze a general iterative algorithm for finding a common solution of a combination of variational inequality problems, a combination of equilibria problem, and a hierarchical fixed point problem in the setting of real Hilbert space.

If γ n = 0, the proposed method is an extension and improvement of the method of Wang and Xu [24] and Bnouhachem [25] for finding the approximate element of the common set of solutions of a combination of variational inequality problems, a combination of equilibria problem and a hierarchical fixed point problem in a real Hilbert space.

In (3.22), if U = 0 then we get the variational inequality 〈 F ( z ), x − z 〉 ≥ 0, ∀ x ∈ F ( T ) ∩ ⋂ i = 1 N EP ( F i ) ⋂ i = 1 N VI ( C, A i ), which just is the variational inequality studied by Suzuki [29] extending the common set of solutions of a combination of variational inequality problems, a combination of equilibria problem, and a hierarchical fixed point problem.

If we have the Lipschitzian mapping U = f, F = I, ρ = μ = 1, and γ n = 0, we obtain an extension and improvement of the method of Yao et al.[13] for finding the approximate element of the common set of solutions of a combination of variational inequality problems, a combination of equilibria problem and a hierarchical fixed point problem in a real Hilbert space.

They also explore the design of policies to avoid the problem of multiple equilibria and indeterminacy.

The problem of multiple equilibria makes it unclear which equilibrium players should focus on, because there is no reasonable way to decide which equilibrium will be selected.

The equilibrium problem contains as special cases, for instance, optimization problems, problems of Nash equilibria, fixed point problems, variational inequalities, and complementarity problems.

Problem (1.3) has useful applications in nonlinear analysis, including optimization problems, variational inequalities, fixed-point problems, and the problems of Nash equilibria as special cases.