相关论文: Nonlinear Perturbation Theory
We construct a sequence that converges to a solution of the Cauchy problem for a singularly perturbed linear inhomogeneous differential equation of an arbitrary order. This sequence is also an asymptotic sequence in the following sense: the…
We develop nonlinear renewal theorems for a perturbed random walk without assuming stochastic boundedness of centered perturbation terms. A second order expansion of the expected stopping time is obtained via the uniform integrability of…
Linear and nonlinear optical effect has been widely discussed in large quantity of materials using theoretical or experimental methods. Except linear optical conductivity, higher-order nonlinear responses are not studied fully. Starting…
The general entire solution to a linear system of moment differential equations is obtained in terms of a moment kernel function for generalized summability, and the Jordan decomposition of the matrix defining the problem. The growth at…
We consider an ordinary nonlinear differential equation with generalized coefficients as an equation in differentials in algebra of new generalized functions. Then the solution of such equation will be a new generalized function. In the…
In this paper, we consider nonlinearly perturbed Legendre differential equations subject to the usual boundary conditions. For such problems we establish sufficient conditions for the existence of solutions and in some cases we provide a…
A unified treatment is given of low-weight modular forms on \Gamma_0(N), N=2,3,4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations,…
In this paper we are interested in obtaining the exact expression and the study of the constant sign of the Green's function related to a second order perturbed periodic problem coupled with integral boundary conditions at the extremes of…
Perturbation or error bounds of functions have been of great interest for a long time. If the functions are differentiable, then the mean value theorem and Taylor's theorem come handy for this purpose. While the former is useful in…
We evaluate the mutual information between the input and the output of a two layer network in the case of a noisy and non-linear analogue channel. In the case where the non-linearity is small with respect to the variability in the noise, we…
A classic problem in analysis is to solve nonlinear equations of the form \begin{equation*} F(x)=0, \end{equation*} where $F:D^n\to \mathbb{R}^m$ is a continuous map of the closed unit disk $D^n\subset\mathbb{R}^n$ in $\mathbb{R}^m$. A…
To have an uniform estimate for the solutions of the scalar curvature equation perturbed by a non linear term, we give some minimal condition on the scalar curvature.
We discuss the occurrence of oscillatory solutions which decay to 0 as $s\to+\infty$ for a class of perturbed second order ordinary differential equations. As opposed to other results in the recent literature, the perturbation is as small…
We present a novel form of relativistic quantum mechanics and demonstrate how to solve it using a recently derived unitary perturbation theory, within partial wave analysis. The theory is tested on a relativistic problem, with two spinless,…
In this paper, we study the existence of solutions for second-order non-instantaneous impulsive differential equations with a perturbation term. By variational approach, we obtain the problem has at least one solution under assumptions that…
This paper presents a full-spectrum Green function methodology (which is valid, in particular, at and around Wood-anomaly frequencies) for evaluation of scattering by periodic arrays of cylinders of arbitrary cross section-with application…
The field-theoretical approach is reviewed. Perturbations in general relativity as well as in an arbitrary $D$-dimensional metric theory are studied on a background, which is a solution (arbitrary) of the theory. Lagrangian for…
We study several enumeration problems connected to linear trees, a broad class which includes stars, paths, generalized stars, and caterpillars. We provide generating functions for counting the number of linear trees on $n$ vertices,…
We introduce the theory of non-linear cosmological perturbations using the correspondence limit of the Schr\"odinger equation. The resulting formalism is equivalent to using the collisionless Boltzman (or Vlasov) equations which remain…
We show that the Green's functions in non-linear gauge in the theory of perturbative quantum gravity is expressed as a series in terms of those in linear gauges. This formulation is also holds for operator Green's functions. We further…