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In this paper, we propose a smoothing method to solve nonlinear complementarity problems involving P 0-functions. We propose a nonparametric algorithm to solve the nonlinear corresponding system of equations and prove some global and local…
Paradoxically, while the assumptions of second-order stationarity and isotropy appear outdated in light of modern spatial data, they remain remarkably robust in practice, as nonstationary methods often provide marginal improvements in…
We compare two different numerical methods to integrate in time spatially delocalized initial densities using the Schr\"odinger-Poisson equation system as the evolution law. The basic equation is a nonlinear Schr\"odinger equation with an…
This paper deals with nonsmooth convex optimization problems in Euclidean spaces. We identify special elements of the subdifferential of a convex function, called specular gradients. Based on this observation, we propose three numerical…
By generalizing the notion of linearization, a concept originally arising from microlocal analysis and symbolic calculus, to diffeological spaces, we make a first proposal setting for optimization problems in this category. We show how…
A functional differential equation related to the logistic equation is studied by a combination of numerical and perturbation methods. Parameter regions are identified where the solution to the nonlinear problem is approximated well by…
We prove the existence of infinitely many high energy sign-changing solutions for some classes of Schrodinger-Poisson systems in bounded domains, with nonlinearities having subcritical or critical growth. Our approach is variational and…
We revisit a formulation technique for inequality constrained optimization problems that has been known for decades: the substitution of squared variables for nonnegative variables. Using this technique, inequality constraints are converted…
In this paper, we consider the problem of minimizing the sum of two convex functions subject to linear linking constraints. The classical alternating direction type methods usually assume that the two convex functions have relatively easy…
We obtain existence and multiplicity results for the solutions of a class of coupled semilinear bi-harmonic Schr\"{o}dinger equations. Actually, using the classical Mountain Pass Theorem and minimization techniques, we prove the existence…
The nonlinear Schr\"odinger and the Schr\"odinger-Newton equations model many phenomena in various fields. Here, we perform an extensive numerical comparison between splitting methods (often employed to numerically solve these equations)…
We have developed a systematic approach to calculate the correlation function for spin-1/2 particles, incorporating both central and noncentral components of the interparticle interaction. This is achieved by extending the variable phase…
In this paper we apply a scaling invariance analysis to reduce a class of parabolic moving boundary problems to free boundary problems governed by ordinary differential equations. As well known free boundary problems are always non-linear…
Cosmological simulations describing the evolution of density perturbations of a self-gravitating collisionless Dark Matter (DM) fluid in an expanding background, provide a powerful tool to follow the formation of cosmic structures over wide…
Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline…
It is established the existence and multiplicity of weak solutions for a class of nonlocal equations involving the fractional laplacian, nonlinearities with critical exponential growth and potentials this is which may change sign. The…
In this paper we introduce a new class of diffeomorphic smoothers based on general spline smoothing techniques and on the use of some tools that have been recently developed in the context of image warping to compute smooth diffeomorphisms.…
We outline a new algorithm to solve coupled systems of differential equations in one continuous variable $x$ (resp. coupled difference equations in one discrete variable $N$) depending on a small parameter $\epsilon$: given such a system…
We aim to solve a structured convex optimization problem, where a nonsmooth function is composed with a linear operator. When opting for full splitting schemes, usually, primal-dual type methods are employed as they are effective and also…
We propose a new variational model in weighted Sobolev spaces with non-standard weights and applications to image processing. We show that these weights are, in general, not of Muckenhoupt type and therefore the classical analysis tools may…