Related papers: Variational principles in quaternionic analysis wi…
In this paper, first some results of [5] are extended for subadditive separating maps between C(X;E) and C(Y;E), such that E is a unital Banach algebra. Then we give some conditions under which a strongly subadditive map has a unique fixed…
Variational quantum Monte Carlo (QMC) is an ab-initio method for solving the electronic Schr\"odinger equation that is exact in principle, but limited by the flexibility of the available ansatzes in practice. The recently introduced deep…
In this paper, we investigate some fixed-point properties of the Mordukhovich differential operator of set valued mappings (or, single valued mappings) on Banach spaces. In particular, we study the fixed-point properties of the Mordukhovich…
Motivated by recent developments in Hamiltonian variational principles, Hamiltonian variational integrators, and their applications such as to optimization and control, we present a new Type II variational approach for Hamiltonian systems,…
Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to the widespread use of variational methods is the lack of…
In this article, we obtain sufficient conditions on existence, uniqueness and Ulam--Hyers stability of solutions for a coupled system of two-point nabla fractional difference boundary value problems, using Banach fixed point theorem and…
We use the direct variational method, the Ekeland variational principle, the mountain pass geometry and Karush-Kuhn-Tucker theorem in order to investigate existence and multiplicity results for boundary value problems connected with the…
We prove a fixed point theorem that combines the contraction mapping principle and some Knaster-Tarski-like theorem. As a consequence we obtain an existence theorem to initial value problem for ordinary differential equation with…
In a variety of scientific applications we wish to characterize a physical system using measurements or observations. This often requires us to solve an inverse problem, which usually has non-unique solutions so uncertainty must be…
By using the recent mathematical tools developed in quaternionic differential operator theory, we solve the Schroedinger equation in presence of a quaternionic step potential. The analytic solution for the stationary states allows to…
The aim of the present paper is to study the existence, uniqueness and some other properties of solutions of a certain partial dynamic integrodifferential equations. The Banach fixed point theorem and certain fundamental inequality with…
Reducibility methods, aiming to simplify systems by conjugating them to those with constant coefficients, are crucial for studying the existence of quasiperiodic solutions. In KAM theory for PDEs, these methods help address the…
This article introduces an innovative mathematical framework designed to tackle non-linear convex variational problems in reflexive Banach spaces. Our approach employs a versatile technique that can handle a broad range of variational…
We prove a unified and general criterion for the uniqueness of critical points of a functional in the presence of constraints such as positivity, boundedness, or fixed mass. Our method relies on convexity properties along suitable paths and…
We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat…
The objective of this work is the construction of `Boyd-Wong fixed point theorem' in the setting of generalized parametric metric space and discussion its application on existence criteria of solutions to a second order initial value…
The successive approximations method allows us to solve problems concerning existence and uniqueness of fixed points of wide classes of operators. The classical result in this field, such as Banach -- Caccioppoli principle together with…
The aim of this article is to study a Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects, degenerate mobility and where only one of the species does separate from the others. We define a notion of weak solution…
A paramount goal in the field of nuclear physics is to unify ab-initio treatments of bound and unbound states. The position-space quantum Monte Carlo (QMC) methods have a long history of successful bound state calculations in light systems…
This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of constrained set-valued mappings/multifunctions between…