Related papers: Measure Differential Equation with a Nonlinear Gro…
We obtain some results of existence and continuity of physical measures through equilibrium states and apply these to non-uniformly expanding transformations on compact manifolds with non-flat critical sets, obtaining sufficient conditions…
In this work, we establish the existence of solutions that change sign at low energy for a non-local weighted Kirchhoff problem in the set $\mathbb{R}^{N}, N>2$. The non-linearity of the equation is assumed to have exponential growth in…
Recently, various systems of nonlinear difference equations, of different forms, were studied. In this existing work, two earlier published papers, due respectively to Bayram and Das. [Appl. Math. Sci. (Ruse), 4(7) (2010) pp. 817-821] and…
We prove strong convergence of a semi-discrete finite difference method for the KdV and modified KdV equations. We extend existing results to non-smooth data (namely, in $L^2$), without size restrictions. Our approach uses a fourth order…
The backward Euler-Maruyama (BEM) method is employed to approximate the invariant measure of stochastic differential equations, where both the drift and the diffusion coefficient are allowed to grow super-linearly. The existence and…
We study a deterministic particle scheme to solve a scalar balance equation with nonlocal interaction and nonlinear mobility used to model congested dynamics. The main novelty with respect to "Radici-Stra [SIAM J. Math. Anal. 55.3 (2023)]"…
In this paper, two tests, based on CUSUM of the residuals and least squares estimation, are studied to detect in real time a change-point in a nonlinear model. A first test statistic is proposed by extension of a method already used in the…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
This paper presents a novel methodology for evaluating the boundedness, stability, and instability of some vector nonlinear systems with multiple time-varying delays and variable coefficients. The proposed technique develops two scalar…
An explicit solution for a growth fragmentation equation with constant dislocation measure is obtained. In this example the necessary condition for the general results in \cite{BW} about the existence of global solutions in the so called…
Given a symmetric Riemannian manifold (M, g), we show some results of genericity for non degenerate sign changing solutions of singularly perturbed nonlinear elliptic problems with respect to the parameters: the positive number {\epsilon}…
We prove existence and uniqueness for some nonlinear stochastic differential equation used in molecular dynamics, whose nonlinearity comes from a conditional expectation term. We also introduce an interacting particle system in order to…
Symmetry preserving difference schemes approximating second and third order ordinary differential equations are presented. They have the same three or four-dimensional symmetry groups as the original differential equations. The new…
This paper investigates the existence of solutions for a class of nonlinear higher-order dynamic equations subject to mixed boundary conditions. We consider boundary value problems in which the nonlinear reaction functions satisfy…
This paper investigates the mean-square exponential stability of neutral stochastic differential delay equations (NSDDEs) with Markovian switching. The analysis addresses the complexities arising from the interaction between the neutral…
We compute the growth fluctuations in equilibrium of a wide class of deposition models. These models also serve as general frame to several nearest-neighbor particle jump processes, e.g. the simple exclusion or the zero range process, where…
We adapt the method of solution regions to prove new existence and localization results for systems of discontinuous differential equations. Some assumptions concerning the definition of a solution region are relaxed and thus our results…
The differential equation (DE) with proportional delay is a particular case of the time-dependent delay differential equation (DDE). In this paper, we solve non-linear DEs with proportional delay using the successive approximation method…
In this paper, we study the eikonal equation in metric measure spaces, where the inhomogeneous term is allowed to be discontinuous, unbounded and merely $p$-integrable in the domain with a finite $p$. For continuous eikonal equations, it is…
Very differently from those perturbative techniques of Deng-Musso in [26], we use the assumption of a $C^1$-stable critical point to construct positive or sign-changing solutions with arbitrary $m$ isolated bubbles to the boundary value…