Related papers: Asymptotic Estimates for Perturbed Scaiar Curvatur…

The paper considers a universal approach that allows one to quite simply obtain nonlinear asymptotic estimates of various summation functions. It is shown the application of this approach to the asymptotic estimation of divergent Dirichlet…

We give a proof of the Kazdan-Warner conjecture concerning the prescribed scalar curvature problem in the null case.

In this paper we investigate the mean square asymptotic stability of a perturbed scalar linear stochastic functional differential equation. Specifically, we are able to give necessary and sufficient conditions on the forcing terms for…

We discuss local linear smooth backfitting for additive non-parametric models. This procedure is well known for achieving optimal convergence rates under appropriate smoothness conditions. In particular, it allows for the estimation of each…

By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…

An adaptive nonparametric estimation procedure is constructed for heteroscedastic regression when the noise variance depends on the unknown regression. A non-asymptotic upper bound for a quadratic risk (oracle inequality) is obtained

We study the existence of a metric with zero scalar curvature maximizing the isoperimetric ratio among all zero scalar curvature metrics in a fixed conformal class of metrics on a compact manifold with boundary. The question may be reduced…

An autonomous system of ordinary differential equations describing nonlinear oscillations on the plane is considered. The influence of time-dependent perturbations decaying at infinity in time is investigated. It is assumed that the…

Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic…

Almost sure bounds are established on the uniform error of smoothing spline estimators in nonparametric regression with random designs. Some results of Einmahl and Mason (2005) are used to derive uniform error bounds for the approximation…

In this note, we investigate the existence of smooth complete hypersurfaces in hyperbolic space with constant $(n-2)$-curvature and a prescribed asymptotic boundary at infinity. Previously, the existence was known only for a restricted…

We consider an undetermined coefficient inverse problem for a nonlinear partial differential equation describing high intensity ultrasound propagation as widely used in medical imaging and therapy. The usual nonlinear term in the standard…

We derive explicit inequalities for sums of eigenvalues of one-dimensional Schr\"{o}dinger operators on the whole line. In the case of the perturbed harmonic oscillator, these bounds converge to the corresponding trace formula in the limit…

We deal with an inverse problem arising in corrosion detection. We prove a stability estimate for a nonlinear term on the inaccessible portion of the boundary by electrostatic boundary measurements on the accessible one.

In this paper, we study time-asymptotic propagation phenomena for a class of dispersive equations on the line by exploiting precise estimates of oscillatory integrals. We propose first an extension of the van der Corput Lemma to the case of…

In this short note, we prove a decay estimate for non-linear solutions of 3D cubic defocusing non-linear Schr\"odinger equation.

A theorem is proved on the uniform estimation of the residual term of the asymptotic expansion with respect to a small parameter of the solution of the initial problem for a singularly perturbed differential operator weakly nonlinear…

This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary…

Perturbed spectra are modelled to estimate OSNR for a single channel amplified link. Perturbation-dependent nonlinear noise is separated from constant ASE noise using a set of propagated perturbed spectra. A least mean square fitting is…

We establish local elliptic and parabolic gradient estimates for positive smooth solutions to a nonlinear parabolic equation on a smooth metric measure space. As applications, we determine various conditions on the equation's coefficients…