Related papers: Some techniques on nonlinear analysis and applicat…
The object of this lecture is to propose a series of conjectures and problems in different fields of analysis. They have been formulated with the aim of introducing some innovative methods in the study of classical topics, as open mappings,…
For nonlinear dispersive systems, the nonlinear Schr\"odinger (NLS) equation can usually be derived as a formal approximation equation describing slow spatial and temporal modulations of the envelope of a spatially and temporally…
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…
The hierarchy of integrable equations are considered. The dynamical approach to the theory of nonlinear waves is proposed. The special solutions(nonlinear waves) of considered equations are derived. We use powerful methods of computer…
The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…
Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate…
The class of nonlinear integral equations on the positive half-line with a monotone operator of Hammerstein type is studied. With various partial representations of the corresponding kernel and nonlinearity, this class of equations has…
We discuss technical results on learning function approximations using piecewise-linear basis functions, and analyze their stability and convergence using nonlinear contraction theory.
The main goal of this paper is to show how some monotonicity methods related with the subdifferential of suitable convex functions and its extensions as m-accretive operators in Banach spaces lead to new and unexpected results showing, for…
Using a multiple critical points theorem for locally Lipschitz continuous functionals, we establish the existence of at least three distinct solutions for a parametric discrete differential inclusion problem involving a real symmetric and…
Unifying several directions of the development of the study of summing multilinear operators between Banach spaces, we construct a general framework that studies, under one single definition, multilinear operators that are summing with…
The goal of this paper is to sketch a broader outline of the mathematical structures present in the Nonlinear Maxwell Theory in continuation of work presented in my previous articles. In particular, I display new types of both dynamic and…
Considering the successful theory of multiple summing multilinear operators as a prototype, we introduce the classes of multiple Cohen strongly p-summing multilinear operators and polynomials. The adequacy of these classes under the…
We examine a recently-proposed family of nonlinear Schr\"odinger equations [J. Phys. A: Math. Gen. 27:1771(1994)] with respect to a group of transformations that linearize a subfamily of them. We investigate the structure of the whole…
We compare the distribution function and the maximum of solutions of nonlinear elliptic equations defined in general domains with solutions of similar problems defined in a ball using Schwarz symmetrization. As an application, we prove the…
A basic idea in optimal transport is that optimizers can be characterized through a geometric property of their support sets called cyclical monotonicity. In recent years, similar "monotonicity principles" have found applications in other…
We introduce a weighted linear dynamic logic (weighted LDL for short) and show the expressive equivalence of its formulas to weighted rational expressions. This adds a new characterization for recognizable series to the fundamental…
The study of token addition and removal and token jumping reconfiguration graphs for power domination is initiated. Some results established here can be extended by applying the methods used for power domination to reconfiguration graphs…
This article presents an identification methodology to capture general relationships, with application to piecewise nonlinear approximations of model predictive control for constrained (non)linear systems. The mathematical formulation…
The purpose of this paper is to present some multidimensional fixed-point theorems and their applications. For this, we provide a multidimensional fixed point theorem and then using this theorem we prove the existence and uniqueness of a…