We consider difference equations with several non-monotone deviating arguments and nonnegative coefficients. The deviations (delays and advances) are, generally, unbounded. Sufficient oscillation conditions are obtained in an explicit iterative form....
Relation between two properties of linear difference equations with infinite delay is investigated: (i) exponential stability, (ii) $ł^p$-input $ł^q$-state stability (sometimes is called Perron's property). The latter means that solutions of the no...
The Bohl-Perron result on exponential dichotomy for a linear difference equation $$ x(n+1)-x(n) + \sum_{l=1}^m a_l(n)x(h_l(n))=0, h_l(n)\leq n, $$ states (under some natural conditions) that if all solutions of the non-homogeneous equation with a b...
We prove that distribution dependent (also called McKean--Vlasov) stochastic delay equations of the form \begin{equation*} \mathrm{d}X(t)= b(t,X_t,\mathcal{L}_{X_t})\mathrm{d}t+ σ(t,X_t,\mathcal{L}_{X_t})\mathrm{d}W(t) \end{equation*} have unique (s...
The paper studies generalized differentiability properties of the marginal function of parametric optimal control problems of semilinear elliptic partial differential equations. We establish upper estimates for the regular and the limiting subgradien...
In this paper, we investigate solution stability for control problems of partial differential equations with the cost functional not involving the usual quadratic term for the control. We first establish a sufficient optimality condition for the opti...
The detection of GW170817 in gravitational waves provides unprecedented constraints on the equation of state (EOS) of the ultra-dense matter within the cores of neutron stars (NSs). We extend the nonparametric analysis first introduced in Landry & Es...
We consider in this paper random batch particle methods for efficiently solving the homogeneous Landau equation in plasma physics. The methods are stochastic variations of the particle methods proposed by Carrillo et al. [J. Comput. Phys.: X 7: 10006...
We study an implicit finite-volume scheme for non-linear, non-local aggregation-diffusion equations which exhibit a gradient-flow structure, recently introduced by Bailo, Carrillo, and Hu (2020). Crucially, this scheme keeps the dissipation property...
In this article we solve a class of two parameter polynomial-quintic equation. The solution follows if we consider the Jacobian elliptic function $sn$ and relate it with the coefficients of the equation. The solution is the elliptic singular modulus...
To our knowledge, there are two main references [9], [12] regarding the periodical solutions of multi-time Euler-Lagrange systems, even if the multi-time equations appeared in 1935, being introduced by de Donder. That is why, the central objective...
A brief survey is presented of our present understanding of the equation-of-state of cold, dense matter and the speed of sound in the interior of neutron stars, based on the constraints inferred from observational data. The second part focuses on str...
We consider the exact rogue periodic wave (rogue wave on the periodic background) and periodic wave solutions for the Chen-Lee-Liu equation via the odd-th order Darboux transformation. Then, the multi-layer physics-informed neural networks (PINNs) de...
Three-term relations of the form AB+CD=EF arise in multiple mathematical contexts, including the Ptolemy equation for a cyclic quadrilateral, Casey's theorem on bitangents, Penner's relation for lambda lengths, and Plücker's identity for the maximal...
In a previous paper Crater and Van Alstine applied the Two Body Dirac equations of constraint dynamics to the meson quark-antiquark bound states using a relativistic extention of the Adler-Piran potential and compared their spectral results to those...
In this article, we study the persistence of properties of a given classical deter-ministic dierential equation under a stochastic perturbation of two distinct forms: external and internal. The rst case corresponds to add a noise term to a given equa...
In recent years, kinetic equations have been used to model many social phenomena. A key feature of these models is that transition rate kernels involve Dirac delta functions, which capture sudden, discontinuous state changes. Here, we study kinetic e...
We present a convergence result for the finite volume method applied to a particular phase field problem suitable for simulation of pure substance solidification. The model consists of the heat equation and the phase field equation with a general for...
We study fluid structure and water-like anomalies of a system constituted by dimeric particles interacting via a purely repulsive core-softened potential by means of integral equation theories. In our model, dimers interact through a repulsive pair p...
We consider the heat equation with a logarithmic nonlinearity, on thereal line. For a suitable sign in front of the nonlinearity, weestablish the existence and uniqueness of solutions of the Cauchyproblem, for a well-adapted class of initial data. Ex...