We consider difference equations in balanced, i.i.d. environments which are not necessary elliptic. In this setting we prove a parabolic Harnack inequality (PHI) for non-negative solutions to the discrete heat equation satisfying (rather mild) growth condition, and identify optimal constant PHI. show by way of an example that condition is our sharp. Along also oscillation (weak) quantitative ho...

Abstract In this paper, we investigate a generalized Camassa–Holm equation. Firstly, establish the persistence properties of strong solutions for equation in weighted spaces $L^{p}_{\phi}=L^{p}(\mathbb{R},\phi ^{p}\,dx)$ L ϕ p = </...

We provide a refined and much more simplified Einstein-Gauss-Bonnet inflationary theoretical framework, which is compatible with the GW170817 observational constraints on gravitational wave speed. As in previous works, constraint that speed $c_T^2=1$ natural units, results to differential equation relates coupling function of scalar field Gauss-Bonnet invariant $\xi(\phi)$ potential $V(\phi)$. ...

In this paper, we establish some sufficient conditions for the existence of a solution equilibrium problem. The problem is understood in general form: find $ \overline{x}\in E such that$ \begin{equation*} \Phi(\overline{x},y) \vartriangleleft (-D\backslash\{0\})^c \text{ all }y \in E; \end{equation*} $and its variants, where Boolean-valued bifunction and \Phi multivalued mapping with values vec...

Our purpose of this paper is to study isolated singular solutions semilinear Helmholtz equation \begin{document}$ -\Delta u-u = Q|u|^{p-1}u \quad{\rm in}\ \ \mathbb{R}^N\setminus\{0\},\ \qquad\lim\limits_{|x|\to0}u(x) +\infty, $\end{document} where N\geq 2 $\end{document}, p&gt;1 and the potential Q: \mathbb{R}^N\to (0,+\infty) a Hölder continuous function satisfying extra decaying conditions a...

This paper studies convergence to equilibrium for the spatially inhomogeneous linear relaxation Boltzmann equation in entropy and related functionals, $p$-entropies. Villani [Hypocoercivity, Memoirs of American Mathematical Society, Vol. 202, Providence, RI, 2006] proved entropic hypocoercivity a class PDEs Hörmander sum-of-squares form. It was an open question prove such result operator which ...

‎In this paper, we study some kinds of majorizations on $textbf{M}_{n}$ and their linear or strong linear preservers. Also, we find the structure of linear or strong linear preservers which are multiplicative, i.e.  linear or strong linear preservers like $Phi $ with the property $Phi (AB)=Phi (A)Phi (B)$ for every $A,Bin textbf{M}_{n}$.