Related papers: Solution Properties for Pertubed Linear and Nonlin…
In this paper, we study existence of solutions to a conformally invariant integral equation involving Poisson-type kernels. Such integral equation has a stronger non-local feature and is not the dual of any PDE. We obtain the existence of…
In the present paper we deal with a quasilinear problem involving a singular term and a parametric superlinear perturbation. We are interested in the existence, nonexistence and multiplicity of positive solutions as the parameter…
In this paper, we study weakly nonlinear boundary value problems on infinite intervals. For such problems, we provide criteria for the existence of solutions as well as a qualitative description of the behavior of solutions depending on a…
We consider eigenvalue condition numbers and backward errors for a class of symmetric nonlinear eigenvalue problems with eigenvector nonlinearities. For both of these quantities, we derive explicit and computable expressions that can be…
Given a solution of a semilinear dispersive partial differential equation with a real analytic nonlinearity, we relate its Cauchy data at two different times by nonlinear representation formulas in terms of convergent series. These series…
We consider the non-stationary Heun equation, also known as quantum Painlev\'e VI, which has appeared in different works on quantum integrable models and conformal field theory. We use a generalized kernel function identity to transform the…
We develop a systematic method to obtain the solution of the collisionless Boltzmann equation which describes the growth of large-scale structures as a perturbative series over the initial density perturbations. We give an explicit…
Nonlinear matrix equations arise in many practical contexts related to control theory, dynamical programming and finite element methods for solving some partial differential equations. In most of these applications, it is needed to compute…
In this paper, a class of high order numerical schemes is proposed to solve the nonlinear parabolic equations with variable coefficients. This method is based on our previous work [10] for convection-diffusion equations, which relies on a…
We consider the inverse problem of determining a general semilinear term appearing in nonlinear parabolic equations. For this purpose, we derive a new criterion that allows to prove global recovery of some general class of semilinear terms…
The inverse medium problem, inherently ill-posed and nonlinear, presents significant computational challenges. This study introduces a novel approach by integrating a Neumann series structure within a neural network framework to effectively…
Spectra of standard 1d potentials (double-well, sin-Gordon etc) are given by trans-series in coupling, including (badly divergent) perturbative series (PS), and nonperturbative terms. All of them are badly defined (e.g. PS are badly…
We provide a systematic formula, in terms of integer partitions, that generates perturbation theory explicitly at an arbitrary order. Our approach naturally includes an infinite number of perturbations and uses a single matrix equation that…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
An algorithm for the numerical solution of a nonlinear integro-differential equation arising in the single-species annihilation reaction $A + A \rightarrow\varnothing$ modeling is discussed. Finite difference method together with the linear…
The goal of this paper is to demonstrate the general modeling and practical simulation of random equations with mixture model parameter random variables. Random equations, understood as stationary (non-dynamical) equations with parameters…
In this paper, we consider a well-known sparse optimization problem that aims to find a sparse solution of a possibly noisy underdetermined system of linear equations. Mathematically, it can be modeled in a unified manner by minimizing…
In analysis, it's often useful to know the value of a function at infinity, this operation possesses pleasant properties. However, even when the limit does not exist, some intuitive considerations may suggest that the function still assumes…
In this paper we present a treatment of hypersingular integrals and integral equations. It is shown the equivalence of different definitions of hypersingular integrals. Then we construct explicit analytical solution to a characteristic…
The perturbed NLS equation is asymptotically integrable if the zero-order approximation to the solution is a single soliton. It is not integrable for any other zero-order solution. In the standard application of a Normal Form expansion,…