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In this paper, we consider a quasi-linear Dirichlet system with possible competing $(p,q)$-Laplacians and convections. Due to the lack of ellipticity, monotonicity, and variational structure, the standard approaches to the existence of weak…
As a sequel to the paper [9], we study the existence and properties of Lipschitz solutions to the initial-boundary value problem of some forward-backward parabolic equations with diffusion fluxes violating Fourier's inequality.
We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.
In this paper we establish existence, uniqueness, and boundedness results for an elliptic variational inequality coupled with a nonlinear ordinary differential equation. Under the general framework, we present a new application modelling…
Based on the theory of invariant sets of descending flow, we give a new proof of the existence of three nontrivial solutions and some remarks on it.
We give a definition for Obstacle Problems with measure data and general obstacles. For such problems we prove existence and uniqueness of solutions and consistency with the classical theory of Variational Inequalities. Continuous…
This paper investigates the inverse problem of determining a general Signorini obstacle using boundary measurements. We demonstrate that both the shape of the obstacle and the obstacle function can be uniquely determined from solution…
This article is concerned with the reconstruction of obstacle $\O$ immersed in a fluid flowing in a bounded domain $\Omega$ in the two dimensional case. We assume that the fluid motion is governed by the Stokes-Brinkmann equations. We make…
A linear system of difference equations and a nonlinear perturbation are considered, we obtain sufficient conditions to ensure the topological equivalence between them, namely, the linear part satisfies a property of dichotomy on the…
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
In this letter, we prove an inequality involving alternating binomial logarithmic sums by exploiting the variance of the logarithm of the maximum of independent and identically distributed exponential random variables. This inequality was…
In this paper, we first present simple proofs of Choi's results [4], then we give a short alternative proof for Fiedler and Markham's inequality [6]. We also obtain additional matrix inequalities related to partial determinants.
In the previous work [Interfaces Free Bound., 19, 351--369, 2017], de Queiroz and Shahgholian established the optimal $C^{1,\log}_{\mathrm{loc}}$ regularity of solutions for the obstacle problem with singular logarithmic forcing term…
We consider an obstacle problem for (possibly non-local) wave equations, and we prove existence of weak solutions through a convex minimization approach based on a time discrete approximation scheme. We provide the corresponding numerical…
We consider a nonlinear Dirichlet problem driven by a variable exponent $p$-Laplacian plus an indefinite potential term. The reaction has the competing effects of a parametric concave (sublinear) term and of a convex (superlinear)…
We consider a diffusion equation with highly oscillatory coefficients that admits a homogenized limit. As an alternative to standard corrector problems, we introduce here an embedded corrector problem, written as a diffusion equation in the…
In this paper we give alternate proofs of some well-known matrix inequalities. In particular, we show that under certain conditions the inequality holds \begin{align}\sum \limits_{\lambda_i\in \mathrm{Spec}(ab^{T})}\mathrm{min}\{\log…
We propose new results for the existence and uniqueness of a general nonparametric and nonseparable competitive equilibrium with substitutes. These results ensure the invertibility of a general competitive system. The existing literature…
In this note we construct an explicit optimal (negative-weight) adversary matrix for the element distinctness problem, given that the size of the alphabet is sufficiently large.
We consider differential-difference equations that determine the continuous symmetries of discrete equations on the triangular lattice. It is shown that a certain combination of continuous flows can be represented as a scalar evolution…