Given a reaction-diffusion system which exhibits Turing’s diffusion-driven instability, we study the influence of unilateral obstacles of opposite sign on bifurcation and critical points. The approach is based on a variational approach to a non-variational problem which even after transformation to a variational problem has an unusual structure for which usual variational methods do not apply.

Variational integrators are symplectic-momentum preserving integrators that are based on a discrete variational formulation of the underlying system. So far, variational integrators have been mainly developed and used for a wide variety of mechanical systems. In this work, we develop a variational integrator for the simulation of electric circuits. An appropriate variational formulation is pres...

Variational inference is a scalable technique for approximate Bayesian inference. Deriving variational inference algorithms requires tedious model-specific calculations; this makes it di cult for non-experts to use. We propose an automatic variational inference algorithm, automatic di erentiation variational inference ( ); we implement it in Stan (code available), a probabilistic programming sy...

Variational inference for latent variable models is prevalent in various machine learning problems, typically solved by maximizing the Evidence Lower Bound (ELBO) of the true data likelihood with respect to a variational distribution. However, freely enriching the family of variational distribution is challenging since the ELBO requires variational likelihood evaluations of the latent variables...

The object of this paper is to establish an existence result for nonlinear inequalities for not necessarily pseudomonotone maps. As a consequence of our result, we give some existence results for variational and variational-like inequalities. Keywords– Nonlinear inequalities, variational inequality problems, variational-like inequality problems, fixed points.

‎This paper is devoted to get a ground state solution for a class of nonlinear elliptic equations with fast increasing weight‎. ‎We apply the variational methods to prove the existence of ground state solution‎.

In this paper, we establish an existence result of the solution for an generalized strong vector variational inequality already considered in the literature and as applications we obtain a new coincidence point theorem in Hilbert spaces.