In recent work, Simsek-Ozdaglar-Acemoglu [5] prove a generalization of the Poincare-Hopf Theorem and establish sufficient conditions for the uniqueness of generalized critical points (generalized equilibria) under some regularity assumptions. In this paper, we restrict ourselves to functions on box-constrained regions and establish the uniqueness of the generalized critical point with weaker re...

We study the uniqueness of weak solutions for Dirichlet problems with variable exponent and non-standard growth conditions. First, we provide two uniqueness results under ellipticity type hypotheses. Next, we provide a uniqueness result when the operator driving the problem is in the form of the divergence of a monotone map. Finally, we derive a fourth uniqueness result under homogeneity type h...

in this paper the fixed point theorem of schauder is used to prove the existence of a continuous solution of the nonlinear fuzzy volterra integral equations. then using some conditions the uniqueness of the solution is investigated.

We establish a one-to-one correspondence between one-sided and two-sided regular systems of conditional probabilities on the half-line that preserves the associated chains and Gibbs measures. As an application, we determine uniqueness and non-uniqueness regimes in one-sided versions of ferromagnetic Ising models with long range interactions. Our study shows that the interplay between chain and ...